Growth: Grades 6+ Math - Algebraic Concepts

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6: Algebraic Concepts

6.1: Patterns, Function Tables, and the Coordinate Plane

6.1.1: Coordinate Geometry

6.1.1.1: [RIT 187 - 208] Interprets points with whole number coordinates in the first quadrant within the given context

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

6.1.1.2: [RIT 198 - 212] Determines the coordinates of points in the first quadrant of a coordinate plane

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

6.1.1.3: [RIT 202 - 210] Plots the coordinates of points in the first quadrant of a coordinate plane

City Tour (Coordinates)
Points in the Coordinate Plane
Points, Lines, and Equations

6.1.1.4: [RIT 206 - 236] Plots points in all four quadrants of a coordinate plane

Points in the Coordinate Plane

6.1.1.5: [RIT 216 - 216] Determines the quadrant for a given ordered pair

Points in the Coordinate Plane

6.1.1.6: [RIT 228 - 228] Plots points to represent solutions to real-world and mathematical problems

Points in the Coordinate Plane

6.1.2: Patterns/Sequences/Series

6.1.2.1: [RIT 165 - 196] Determines the single-step rule, and extends or finds a missing term for number patterns involving addition 

Finding Patterns

6.1.2.2: [RIT 167 - 197] Determines the single-step rule for number patterns involving addition or subtraction 

Finding Patterns

6.1.2.3: [RIT 168 - 210] Determines the rule, and extends or finds a missing term for repeating shape patterns

Pattern Flip (Patterns)

6.1.2.4: [RIT 175 - 201] Determines missing values in a table representing a proportional relationship, given the function rule

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Points, Lines, and Equations

6.1.2.5: [RIT 176 - 188] Determines the single-step rule, and extends or finds a missing term for number patterns involving models  

Finding Patterns

6.1.2.6: [RIT 179 - 179] Creates or extends repeating shape patterns, given the rule

Pattern Flip (Patterns)

6.1.2.7: [RIT 183 - 230] Analyzes and describes patterns without stating the rule 

Finding Patterns
Pattern Flip (Patterns)

6.1.2.8: [RIT 183 - 220] Determines missing values in a table representing a proportional relationship, function rule not given

Function Machines 1 (Functions and Tables)

6.1.2.9: [RIT 185 - 206] Determines the single-step rule, and extends or finds a missing term for number patterns involving subtraction  

Arithmetic Sequences

6.1.2.10: [RIT 187 - 233] Determines missing values in a function table representing a nonproportional relationship, given the rule

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Points, Lines, and Equations

6.1.2.11: [RIT 191 - 195] Determines the two-step rule for number patterns involving multiple operations 

Function Machines 3 (Functions and Problem Solving)

6.1.2.12: [RIT 191 - 207] Creates or extends number patterns, given the rule

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)

6.1.2.14: [RIT 193 - 217] Determines the rule, and extends or finds a missing term for growing/shrinking shape patterns

Finding Patterns

6.1.2.17: [RIT 195 - 233] Determines the two-step rule, and extends or finds a missing term for number patterns involving multiple operations

Function Machines 3 (Functions and Problem Solving)

6.1.2.18: [RIT 197 - 227] Determines the rule for growing/shrinking shape patterns

Finding Patterns

6.1.2.20: [RIT 201 - 201] Determines the single-step rule for number patterns involving multiplication or division 

Function Machines 1 (Functions and Tables)

6.1.2.21: [RIT 202 - 218] Determines the rule for a given function table representing a proportional relationship

Function Machines 1 (Functions and Tables)

6.1.2.23: [RIT 205 - 219] Determines the single-step rule, and extends or finds a missing term for number patterns involving multiplication or division 

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)

6.1.2.24: [RIT 205 - 226] Determines the rule for a given function table representing a nonproportional relationship

Function Machines 1 (Functions and Tables)

6.1.2.26: [RIT 210 - 228] Identifies a function table that matches a given rule

Points, Lines, and Equations

6.1.2.28: [RIT 215 - 218] Determines the rule, and extends or finds a missing term given descriptions of number patterns within a real-world context

Function Machines 1 (Functions and Tables)
Function Machines 3 (Functions and Problem Solving)

6.1.2.30: [RIT 223 - 258] Determines the value of a term in an arithmetic sequence given a contextual situation

Arithmetic Sequences

6.1.2.31: [RIT 227 - 232] Determines the single-step rule, and extends or finds a missing term for number patterns involving fractions 

Function Machines 1 (Functions and Tables)

6.1.2.32: [RIT 229 - 266] Determines the value of a term in a geometric sequence given a contextual situation

Geometric Sequences

6.1.2.34: [RIT 232 - 238] Recognizes arithmetic sequences

Arithmetic Sequences
Arithmetic and Geometric Sequences

6.1.2.35: [RIT 235 - 256] Determines the rule, and extends or finds a missing term in a Fibonacci sequence

Arithmetic Sequences

6.1.2.38: [RIT 243 - 275] Writes an expression or formula for the nth term of an arithmetic sequence given a number sequence

Arithmetic and Geometric Sequences

6.1.2.39: [RIT 252 - 252] Determines the rule, and extends or finds a missing term for number patterns which increase or decrease by a nonconstant amount, within a real-world context

Arithmetic Sequences

6.1.2.40: [RIT 253 - 285] Determines the value of a term in a geometric sequence defined by a list

Arithmetic and Geometric Sequences
Geometric Sequences

6.1.2.41: [RIT 256 - 256] Determines the common ratio in a geometric sequence

Geometric Sequences

6.1.2.43: [RIT 260 - 271] Writes an expression or formula for the nth term of a geometric sequence given a number sequence

Arithmetic and Geometric Sequences
Geometric Sequences

6.2: Expressions

6.2.1: Algebraic Expressions

6.2.1.1: [RIT 212 - 240] Writes linear expressions in one variable to represent real-world or mathematical contexts

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

6.2.1.3: [RIT 213 - 246] Evaluates linear expressions at given values with variables involving positive rational numbers

Equivalent Algebraic Expressions I

6.2.1.4: [RIT 216 - 247] Translates between verbal and algebraic expressions

Using Algebraic Expressions

6.2.1.5: [RIT 220 - 248] Generates equivalent linear expressions by using the associative, commutative, or distributive property

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

6.2.1.8: [RIT 226 - 249] Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

6.2.1.9: [RIT 227 - 242] Generates equivalent linear expressions by combining like terms

Simplifying Algebraic Expressions II

6.2.1.10: [RIT 232 - 268] Adds and subtracts polynomials

Addition and Subtraction of Functions
Addition of Polynomials

6.2.1.11: [RIT 232 - 261] Multiplies a polynomial by a monomial

Polynomials and Linear Factors

6.2.1.12: [RIT 233 - 233] Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

6.2.1.13: [RIT 236 - 263] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

6.2.1.14: [RIT 237 - 260] Multiplies two binomial expressions

Factoring Special Products
Modeling the Factorization of x2+bx+c
Quadratics in Polynomial Form

6.2.1.15: [RIT 237 - 262] Evaluates nonlinear expressions at given values with variables involving negative rational numbers

Exponential Growth and Decay
General Form of a Rational Function
Quadratics in Polynomial Form

6.2.1.16: [RIT 238 - 252] Factors polynomials using a difference of squares

Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

6.2.1.17: [RIT 239 - 261] Factors quadratic trinomials

Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

6.2.1.18: [RIT 239 - 239] Generates equivalent nonlinear expressions by combining like terms

Simplifying Algebraic Expressions II

6.2.1.19: [RIT 239 - 257] Multiplies monomials

Multiplying Exponential Expressions

6.2.1.20: [RIT 240 - 240] Writes algebraic expressions from a mathematical description of its component parts, including sum, product, quotient, term, and coefficient

Using Algebraic Expressions

6.2.1.21: [RIT 242 - 242] Interprets the variable in a linear expression within the context of a real-world relationship

Slope-Intercept Form of a Line

6.2.1.23: [RIT 244 - 244] Determines the number of terms in a polynomial

Polynomials and Linear Factors

6.2.1.24: [RIT 244 - 273] Simplifies rational expressions

General Form of a Rational Function

6.2.1.25: [RIT 245 - 248] Uses algebra tiles to model polynomials

Addition of Polynomials
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

6.2.1.28: [RIT 251 - 283] Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero

Dividing Exponential Expressions
Exponents and Power Rules

6.2.1.31: [RIT 254 - 269] Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms

Multiplying Exponential Expressions

6.2.1.33: [RIT 256 - 263] Multiplies polynomials

Factoring Special Products

6.2.1.34: [RIT 256 - 256] Interprets the constant in a quadratic expression within the context of a real-world relationship

Quadratics in Polynomial Form

6.2.1.35: [RIT 260 - 260] Writes a rational expression as a sum of a polynomial and a proper rational expression

Dividing Polynomials Using Synthetic Division

6.2.1.37: [RIT 263 - 263] Writes linear expressions in two variables to represent real-world or mathematical contexts

Standard Form of a Line

6.2.1.39: [RIT 265 - 274] Writes quadratic expressions in one variable to represent real-world or mathematical contexts

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

6.2.1.40: [RIT 265 - 270] Squares binomial expressions

Factoring Special Products

6.2.1.43: [RIT 271 - 271] Writes rational expressions in one variable to represent real-world or mathematical contexts

Direct and Inverse Variation
General Form of a Rational Function
Rational Functions

6.2.2: Numerical Expressions

6.2.2.1: [RIT 173 - 199] Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses

Equivalent Algebraic Expressions I

6.2.2.2: [RIT 196 - 235] Evaluates numerical expressions involving multiple operations with whole numbers and parentheses

Order of Operations

6.2.2.4: [RIT 211 - 230] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers

Order of Operations

6.2.2.5: [RIT 215 - 215] Represents real-world problems involving the addition and subtraction of integers with numerical expressions

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips

6.2.2.6: [RIT 217 - 240] Evaluates numerical expressions involving multiple operations with whole numbers, no parenthesis

Order of Operations

6.2.2.8: [RIT 218 - 264] Uses properties of exponents to simplify numerical expressions involving whole-number exponents only

Exponents and Power Rules
Multiplying Exponential Expressions

6.2.2.9: [RIT 218 - 218] Evaluates numerical expressions involving addition and subtraction with whole numbers, no parentheses

Adding and Subtracting Integers

6.2.2.10: [RIT 220 - 240] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving both positive and negative rational numbers

Order of Operations

6.2.2.11: [RIT 223 - 243] Applies the order of operations, with grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers

Order of Operations

6.2.2.12: [RIT 224 - 245] Applies the order of operations, without grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers

Order of Operations

6.2.2.14: [RIT 229 - 255] Rewrites the sum of two whole numbers as a product of a common factor and the sum of two whole numbers

Equivalent Algebraic Expressions II

6.2.2.17: [RIT 237 - 279] Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero

Exponents and Power Rules

6.2.2.18: [RIT 238 - 243] Applies the order of operations, without grouping symbols or whole-number exponents, to simplify numerical expressions involving positive rational numbers

Order of Operations

6.2.2.20: [RIT 257 - 257] Represents descriptions of exponential growth with numerical expressions

Compound Interest
Exponential Growth and Decay

6.2.3: Exponents

6.2.3.1: [RIT 218 - 264] Uses properties of exponents to simplify numerical expressions involving whole-number exponents only

Exponents and Power Rules
Multiplying Exponential Expressions

6.2.3.2: [RIT 236 - 263] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

6.2.3.3: [RIT 237 - 279] Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero

Exponents and Power Rules

6.2.3.4: [RIT 251 - 283] Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero

Dividing Exponential Expressions
Exponents and Power Rules

6.3: Equations and Inequalities

6.3.1: Inequalities

6.3.1.1: [RIT 216 - 234] Determines whether a linear equation or inequality is true for a given value of the variable

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.2: [RIT 221 - 243] Identifies an ordered pair that is a solution to a two-variable linear inequality

Linear Inequalities in Two Variables

6.3.1.3: [RIT 227 - 249] Writes a one-step linear inequality in one variable to represent a real-world or mathematical context

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.4: [RIT 228 - 243] Writes a multi-step linear inequality in one variable to represent a real-world or mathematical context

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.5: [RIT 229 - 229] Solves one-step linear inequalities with positive rational numbers

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.7: [RIT 231 - 260] Writes a compound inequality to represent a real-world or mathematical context

Compound Inequalities

6.3.1.8: [RIT 232 - 232] Writes a quadratic inequality in one variable to represent a real-world or mathematical context

Quadratic Inequalities

6.3.1.9: [RIT 233 - 234] Writes a linear inequality in two variables to represent a real-world or mathematical context

Linear Inequalities in Two Variables

6.3.1.10: [RIT 233 - 257] Solves two-step linear inequalities

Exploring Linear Inequalities in One Variable

6.3.1.11: [RIT 236 - 246] Writes and solves a one-step linear inequality in one variable involving a real-world or mathematical context

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.12: [RIT 236 - 253] Solves one-step linear inequalities with negative rational numbers

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.13: [RIT 238 - 243] Writes an inequality in the form x > c or x < c to represent a real-world or mathematical context

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.14: [RIT 239 - 239] Writes a linear inequality to represent a region on the coordinate plane

Linear Inequalities in Two Variables

6.3.1.16: [RIT 241 - 250] Represents the solutions of a compound linear inequality on a number line

Compound Inequalities

6.3.1.17: [RIT 241 - 246] Represents the solutions of a one-step linear inequality on a number line

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.18: [RIT 243 - 243] Represents an inequality in the form x > c or x < c on a number line given a real-world or mathematical context

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.19: [RIT 243 - 262] Solves multi-step linear inequalities

Exploring Linear Inequalities in One Variable

6.3.1.20: [RIT 244 - 251] Writes an inequality in the form x > c or x < c to represent a set of real numbers shown on a number line

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.1.21: [RIT 244 - 254] Represents the solutions of a two-step linear inequality on a number line

Exploring Linear Inequalities in One Variable

6.3.1.22: [RIT 244 - 271] Represents the solutions of an absolute value inequality on a number line

Absolute Value Equations and Inequalities

6.3.1.25: [RIT 248 - 253] Determines whether an absolute value equation or inequality is true for a given value of the variable

Absolute Value Equations and Inequalities

6.3.1.26: [RIT 255 - 255] Represents a compound inequality on a number line given a real-world or mathematical context

Compound Inequalities

6.3.1.27: [RIT 257 - 266] Solves compound linear inequalities

Compound Inequalities

6.3.1.28: [RIT 259 - 264] Represents the solutions of a two-variable linear inequality on the coordinate plane

Linear Inequalities in Two Variables

6.3.1.29: [RIT 260 - 275] Solves absolute value inequalities

Absolute Value Equations and Inequalities

6.3.1.30: [RIT 260 - 264] Represents the solutions of a multistep linear inequality on a number line

Exploring Linear Inequalities in One Variable

6.3.1.31: [RIT 263 - 263] Solves quadratic inequalities

Quadratic Inequalities

6.3.1.33: [RIT 268 - 268] Represents the solutions of a two-variable quadratic inequality on the coordinate plane

Quadratic Inequalities

6.3.1.34: [RIT 270 - 275] Writes an absolute value inequality to represent a real-world or mathematical context

Absolute Value Equations and Inequalities

6.3.2: Number Sentences/Equations/Equivalence

6.3.2.1: [RIT 158 - 185] Determines unknown parts in addition equations with whole numbers, sums within 20

Modeling One-Step Equations
Number Line Frog Hop (Addition and Subtraction)
Solving Algebraic Equations II

6.3.2.2: [RIT 167 - 199] Determines unknown parts in addition equations with whole numbers, sums within 100

Modeling One-Step Equations
Number Line Frog Hop (Addition and Subtraction)
Solving Algebraic Equations II

6.3.2.3: [RIT 167 - 181] Determines start or change unknown in subtraction equations with whole numbers within 20

Modeling One-Step Equations
Number Line Frog Hop (Addition and Subtraction)

6.3.2.4: [RIT 169 - 185] Determines start or change unknown in subtraction equations with whole numbers within 100

Number Line Frog Hop (Addition and Subtraction)

6.3.2.5: [RIT 173 - 245] Solves one-step linear equations with positive rational numbers

Solving Algebraic Equations II
Solving Equations on the Number Line

6.3.2.6: [RIT 174 - 210] Determines unknown factors in multiplication equations with whole numbers and products within 100

Factor Trees (Factoring Numbers)

6.3.2.7: [RIT 176 - 200] Identifies equivalent whole-number addition or subtraction expressions

Equivalent Algebraic Expressions I
Number Line Frog Hop (Addition and Subtraction)

6.3.2.8: [RIT 182 - 199] Determines unknown parts in addition equations with whole numbers, sums greater than 100

Target Sum Card Game (Multi-digit Addition)

6.3.2.9: [RIT 183 - 183] Identifies true one-step addition and subtraction equations involving whole numbers

Number Line Frog Hop (Addition and Subtraction)

6.3.2.10: [RIT 186 - 186] Determines start or change unknown in addition equations with decimals

Solving Equations on the Number Line

6.3.2.13: [RIT 194 - 228] Determines unknown parts in multi-step equations with whole numbers

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Two-Step Equations

6.3.2.18: [RIT 202 - 229] Solves problems involving equations represented on a balanced scale

Solving Two-Step Equations

6.3.2.19: [RIT 203 - 214] Identifies true multi-step addition and subtraction equations with whole numbers

Modeling and Solving Two-Step Equations

6.3.2.20: [RIT 204 - 204] Translates between verbal and algebraic equations

Using Algebraic Expressions

6.3.2.22: [RIT 206 - 239] Solves one-step linear equations with negative rational numbers

Solving Equations on the Number Line

6.3.2.23: [RIT 211 - 217] Determines unknown parts in multi-step equations with whole numbers and parentheses

Solving Algebraic Equations II

6.3.2.25: [RIT 213 - 242] Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations
Using Algebraic Equations

6.3.2.27: [RIT 216 - 248] Solves two-step linear equations with positive rational numbers

Solving Algebraic Equations II

6.3.2.28: [RIT 216 - 229] Writes a one-step linear equation in one variable to represent a real-world or mathematical context

Solving Equations on the Number Line
Using Algebraic Equations

6.3.2.29: [RIT 216 - 234] Determines whether a linear equation or inequality is true for a given value of the variable

Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

6.3.2.31: [RIT 219 - 219] Determines unknown parts in addition equations with fractions, like denominators

Solving Algebraic Equations II

6.3.2.32: [RIT 221 - 275] Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method

Quadratics in Factored Form
Roots of a Quadratic

6.3.2.33: [RIT 224 - 248] Determines unknown factors in multiplication equations with fractions

Multiplying Fractions
Solving Algebraic Equations II

6.3.2.34: [RIT 226 - 259] Solves multi-step linear equations with positive and negative rational numbers

Solving Algebraic Equations II
Solving Equations on the Number Line

6.3.2.35: [RIT 226 - 247] Solves two-step linear equations with negative rational numbers

Solving Equations on the Number Line

6.3.2.36: [RIT 226 - 265] Solves absolute value equations

Absolute Value Equations and Inequalities

6.3.2.38: [RIT 232 - 253] Determines unknown dividends or divisors in division equations with fractions

Dividing Fractions

6.3.2.39: [RIT 232 - 242] Evaluates formulas or linear equations at given values for the variables

Area of Parallelograms
Area of Triangles
Distance Formula
Equivalent Algebraic Expressions I

6.3.2.40: [RIT 235 - 262] Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context

Quadratics in Factored Form
Roots of a Quadratic

6.3.2.41: [RIT 236 - 253] Writes a multi-step linear equation in one variable to represent a real-world or mathematical context

Solving Equations on the Number Line

6.3.2.42: [RIT 239 - 239] Applies the multiplicative property of equality when solving an equation

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

6.3.2.43: [RIT 239 - 240] Writes a two-step linear equation in one variable to represent a real-world or mathematical context

Modeling and Solving Two-Step Equations
Solving Equations on the Number Line
Solving Two-Step Equations
Using Algebraic Equations

6.3.2.44: [RIT 240 - 267] Solves radical equations that lead to linear equations

Radical Functions

6.3.2.45: [RIT 240 - 240] Writes the equation of a vertical line given a graph

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

6.3.2.47: [RIT 241 - 247] Applies the simple interest formula to solve for the interest rate, principal, or time invested

Compound Interest

6.3.2.48: [RIT 242 - 274] Writes and solves a multi-step linear equation in one variable involving a real-world or mathematical context

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

6.3.2.49: [RIT 243 - 264] Solves literal equations for linear variables

Solving Formulas for any Variable

6.3.2.51: [RIT 245 - 245] Determines unknown parts in addition equations with fractions, unlike denominators

Fractions with Unlike Denominators

6.3.2.52: [RIT 246 - 266] Identifies an ordered pair that is a solution to a two-variable equation

Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

6.3.2.53: [RIT 248 - 253] Determines whether an absolute value equation or inequality is true for a given value of the variable

Absolute Value Equations and Inequalities

6.3.2.54: [RIT 248 - 279] Writes a quadratic equation in one variable to represent a real-world or mathematical context

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

6.3.2.55: [RIT 249 - 251] Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision

Solving Equations by Graphing Each Side

6.3.2.57: [RIT 250 - 250] Understands the slope of a vertical line is undefined

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

6.3.2.59: [RIT 254 - 270] Solves quadratic equations with complex solutions

Roots of a Quadratic

6.3.2.60: [RIT 254 - 264] Determines the nature of the solutions of a quadratic equation

Roots of a Quadratic

6.3.2.61: [RIT 257 - 257] Solves polynomial equations

Graphs of Polynomial Functions

6.3.2.62: [RIT 257 - 297] Solves literal equations for nonlinear variables

Distance Formula

6.3.2.63: [RIT 258 - 258] Writes an absolute value equation in one variable to represent a real-world or mathematical context

Absolute Value Equations and Inequalities

6.3.2.66: [RIT 268 - 268] Writes and solves an exponential equation in one variable involving a real-world or mathematical context

Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions

6.3.2.68: [RIT 276 - 276] Writes an exponential equation in one variable to represent a real-world or mathematical context

Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions

6.3.2.69: [RIT 278 - 278] Understands the relationship between the discriminant and the nature of solutions

Roots of a Quadratic

6.3.3: Decimals: Represent and Solve Word Problems

6.3.3.1: [RIT 200 - 200] Represents one-step word problems with expressions or equations and involving decimals with the same number of digits after the decimal point, including contexts involving money

Multiplying Decimals (Area Model)
Multiplying with Decimals

6.4: System of Equations and Inequalities

6.4.1: System of Equations/Inequalities

6.4.1.1: [RIT 195 - 204] Solves a system of linear equations involving a real-world context, given a table

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.2: [RIT 215 - 256] Writes and solves a system of linear equations involving a real-world or mathematical context

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.3: [RIT 217 - 238] Solves a system of linear equations graphically

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.4: [RIT 230 - 254] Writes a system of linear equations to represent a real-world or mathematical context

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.5: [RIT 236 - 261] Solves a system of linear equations algebraically

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.6: [RIT 238 - 257] Identifies an ordered pair that is a solution to a system of linear inequalities

Systems of Linear Inequalities (Slope-intercept form)

6.4.1.7: [RIT 240 - 240] Solves a system of linear inequalities

Systems of Linear Inequalities (Slope-intercept form)

6.4.1.8: [RIT 240 - 253] Writes a system of linear inequalities to represent a real-world or mathematical context

Systems of Linear Inequalities (Slope-intercept form)

6.4.1.10: [RIT 250 - 257] Shows the steps to solve a system of linear equations using linear combinations

Solving Linear Systems (Standard Form)

6.4.1.13: [RIT 251 - 262] Graphs a system of linear inequalities

Systems of Linear Inequalities (Slope-intercept form)

6.4.1.14: [RIT 252 - 274] Solves a system of linear equations given a table

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.15: [RIT 253 - 261] Shows the steps to solve a system of linear equations using the substitution method

Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.16: [RIT 257 - 257] Writes a system of linear inequalities given a graph

Systems of Linear Inequalities (Slope-intercept form)

6.4.1.17: [RIT 259 - 261] Writes a system of linear equations given a graph

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.18: [RIT 259 - 259] Graphs a system of linear equations

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

6.4.1.22: [RIT 277 - 277] Solves real-world problems involving rates and distances that lead to a system of linear equations

Cat and Mouse (Modeling with Linear Systems)

6.5: Linear Functions, Slope, and Rate of Change

6.5.1: Rate of Change/Slope

6.5.1.1: [RIT 202 - 249] Compares the rate of change between two proportional relationships represented in different ways

Direct and Inverse Variation

6.5.1.2: [RIT 212 - 255] Interprets the meaning of the slope of a graph in a real-world linear relationship

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)

6.5.1.3: [RIT 215 - 244] Calculates the rate of change from a table or description of a real-world linear relationship

Direct and Inverse Variation
Distance-Time Graphs
Slope-Intercept Form of a Line

6.5.1.4: [RIT 216 - 222] Identifies the unit rate from the graph of a proportional relationship

Direct and Inverse Variation

6.5.1.5: [RIT 216 - 223] Determines the coordinates of the point representing the unit rate on a graph of a proportional relationship

Direct and Inverse Variation

6.5.1.6: [RIT 220 - 236] Calculates the rate of change from a graph representing a real-world linear relationship

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)

6.5.1.7: [RIT 232 - 243] Compares the rate of change and intercepts between two nonproportional linear functions represented in the same way

Point-Slope Form of a Line
Standard Form of a Line

6.5.1.8: [RIT 233 - 233] Interprets the meaning of the slope and y-intercept of a graph within the context of a real-world linear relationship

Slope-Intercept Form of a Line

6.5.1.10: [RIT 236 - 257] Calculates the rate of change of a piecewise function over a given interval

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)

6.5.1.11: [RIT 237 - 250] Identifies the y-intercept and the slope of a line given an equation of the line in the form y = mx + b

Point-Slope Form of a Line
Slope-Intercept Form of a Line

6.5.1.12: [RIT 238 - 258] Understands that the slope is the same between any two points on a line

Slope-Intercept Form of a Line

6.5.1.13: [RIT 239 - 262] Determines the y-intercept and the slope of a line given an equation of the line in a form other than y = mx + b

Point-Slope Form of a Line
Standard Form of a Line

6.5.1.14: [RIT 246 - 246] Interprets the meaning of the slope for the equation y = mx + b within the context of a real-world linear relationship

Slope-Intercept Form of a Line

6.5.1.15: [RIT 247 - 253] Calculates the slope of a line on a graph

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope

6.5.1.16: [RIT 248 - 259] Calculates the slope of a line given ordered pairs

Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

6.5.2: Linear Functions

6.5.2.1: [RIT 193 - 206] Expresses the linear relationship between variables in words

Points, Lines, and Equations
Slope-Intercept Form of a Line

6.5.2.2: [RIT 202 - 249] Compares the rate of change between two proportional relationships represented in different ways

Direct and Inverse Variation

6.5.2.4: [RIT 212 - 255] Interprets the meaning of the slope of a graph in a real-world linear relationship

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)

6.5.2.5: [RIT 212 - 249] Translates between the graph of a piecewise linear function and a verbal description of the real-world relationship

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

6.5.2.6: [RIT 212 - 233] Graphs a linear function of the form y = mx given a simple scenario

Direct and Inverse Variation

6.5.2.7: [RIT 215 - 244] Calculates the rate of change from a table or description of a real-world linear relationship

Direct and Inverse Variation
Distance-Time Graphs
Slope-Intercept Form of a Line

6.5.2.8: [RIT 219 - 234] Identifies the table of values given a graph of a linear relationship in the form y = mx + b

Points, Lines, and Equations
Slope-Intercept Form of a Line

6.5.2.9: [RIT 220 - 236] Calculates the rate of change from a graph representing a real-world linear relationship

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)

6.5.2.10: [RIT 221 - 259] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given the slope and y-intercept

Slope-Intercept Form of a Line

6.5.2.11: [RIT 222 - 259] Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs

Slope-Intercept Form of a Line

6.5.2.12: [RIT 224 - 224] Understands independent and dependent variables within a linear context

Linear Functions

6.5.2.14: [RIT 226 - 240] Writes an equation in the form y = mx to represent the relationship between real-world quantities given a simple scenario

Direct and Inverse Variation

6.5.2.16: [RIT 229 - 237] Translates between the graph of a linear function and a verbal description of the real-world relationship

Slope-Intercept Form of a Line

6.5.2.19: [RIT 231 - 234] Graphs a linear function of the form y = mx + b given a table of values

Slope-Intercept Form of a Line

6.5.2.20: [RIT 231 - 242] Describes a situation that can be represented by a given linear equation

Slope-Intercept Form of a Line

6.5.2.22: [RIT 232 - 243] Compares the rate of change and intercepts between two nonproportional linear functions represented in the same way

Point-Slope Form of a Line
Standard Form of a Line

6.5.2.23: [RIT 233 - 233] Interprets the meaning of the slope and y-intercept of a graph within the context of a real-world linear relationship

Slope-Intercept Form of a Line

6.5.2.24: [RIT 233 - 253] Interprets the meaning of the y-intercept of a graph within the context of a real-world linear relationship

Slope-Intercept Form of a Line

6.5.2.27: [RIT 235 - 243] Interprets the meaning of the constant term in the equation y = mx + b within the context of a real-world linear relationship

Slope-Intercept Form of a Line

6.5.2.28: [RIT 235 - 259] Writes the equation of a line in standard form given a table of values or two ordered pairs

Standard Form of a Line

6.5.2.29: [RIT 235 - 235] Identifies an intercept of a graph of a linear function

Standard Form of a Line

6.5.2.32: [RIT 237 - 250] Identifies the y-intercept and the slope of a line given an equation of the line in the form y = mx + b

Point-Slope Form of a Line
Slope-Intercept Form of a Line

6.5.2.34: [RIT 237 - 274] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given the slope and a point on the line

Slope-Intercept Form of a Line

6.5.2.35: [RIT 238 - 258] Understands that the slope is the same between any two points on a line

Slope-Intercept Form of a Line

6.5.2.36: [RIT 238 - 253] Solves direct variation problems

Direct and Inverse Variation

6.5.2.37: [RIT 239 - 239] Describes the effects of changes in parameters on linear functions that represent real-world relationships

Direct and Inverse Variation
Slope-Intercept Form of a Line
Standard Form of a Line

6.5.2.38: [RIT 239 - 262] Determines the y-intercept and the slope of a line given an equation of the line in a form other than y = mx + b

Point-Slope Form of a Line
Standard Form of a Line

6.5.2.40: [RIT 240 - 240] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given a simple scenario

Direct and Inverse Variation
Slope-Intercept Form of a Line

6.5.2.41: [RIT 240 - 254] Graphs the equation of a line in the form y = mx + b

Slope-Intercept Form of a Line

6.5.2.45: [RIT 243 - 243] Recognizes direct variation situations

Direct and Inverse Variation

6.5.2.46: [RIT 245 - 261] Describes the effects that changes in the constant terms have on the graphs of linear functions

Slope-Intercept Form of a Line

6.5.2.48: [RIT 246 - 246] Interprets the meaning of the slope for the equation y = mx + b within the context of a real-world linear relationship

Slope-Intercept Form of a Line

6.5.2.50: [RIT 247 - 253] Calculates the slope of a line on a graph

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope

6.5.2.51: [RIT 248 - 259] Calculates the slope of a line given ordered pairs

Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

6.5.2.52: [RIT 250 - 267] Illustrates the result of changes in the slope and y-intercept within a real-world linear relationship

Slope-Intercept Form of a Line

6.5.2.53: [RIT 250 - 250] Determines the y-intercept of a line given two points on the line

Points, Lines, and Equations

6.5.2.54: [RIT 253 - 253] Rewrites a linear equation in the form y = mx + b

Point-Slope Form of a Line
Standard Form of a Line

6.5.2.55: [RIT 253 - 253] Graphs the equation of a line in standard form

Standard Form of a Line

6.5.2.57: [RIT 255 - 269] Rewrites a linear equation into the form Ax + By = C

Standard Form of a Line

6.5.2.58: [RIT 255 - 255] Represents a proportional relationship in more than one form, including tables, graphs, equations, and verbal descriptions

Direct and Inverse Variation

6.5.2.60: [RIT 257 - 257] Writes the equation of a line in the form y = mx + b given the slope and a point on the line

Slope-Intercept Form of a Line

6.5.2.62: [RIT 268 - 268] Writes the equation of a line in standard form given the slope and y-intercept

Standard Form of a Line

6.5.2.63: [RIT 268 - 268] Writes the equation of a line in standard form given the slope and a point on the line

Standard Form of a Line

6.5.2.64: [RIT 273 - 273] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given a complex scenario

Slope-Intercept Form of a Line

6.6: Nonlinear Functions

6.6.1: Polynomial Functions

6.6.1.1: [RIT 262 - 274] Factors polynomial functions to determine zeros

Polynomials and Linear Factors

6.6.1.3: [RIT 267 - 267] Evaluates a polynomial function using synthetic division

Dividing Polynomials Using Synthetic Division

6.6.1.4: [RIT 270 - 270] Describes the effects of transformations on the graphs of polynomial functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

Quadratics in Polynomial Form
Quadratics in Vertex Form
Translating and Scaling Functions

6.6.1.5: [RIT 270 - 270] Identifies key features of a polynomial function given a graph

Graphs of Polynomial Functions
Polynomials and Linear Factors

6.6.1.6: [RIT 281 - 281] Writes the equation of a polynomial in terms of its linear factors, including factors with a multiplicity greater than 1, given a graph

Polynomials and Linear Factors
Quadratics in Factored Form

6.6.1.7: [RIT 284 - 286] Identifies the factors of a polynomial function from a graph

Polynomials and Linear Factors

6.6.2: Trigonometric Functions/Radian Measure

6.6.2.1: [RIT 241 - 251] Converts between radians and degrees

Cosine Function
Sine Function
Tangent Function

6.6.2.2: [RIT 252 - 276] Understands the relationship between radian measure and the length of an arc on the unit circle

Cosine Function
Radians
Sine Function
Tangent Function

6.6.2.3: [RIT 261 - 276] Uses special right triangles and the unit circle to determine a value of tangent

Tangent Function

6.6.2.4: [RIT 266 - 276] Uses special right triangles and the unit circle to determine a value of cosine

Cosine Function

6.6.2.5: [RIT 284 - 284] Determines the sign of trigonometric values within a given range of angle measures

Cosine Function
Sine Function
Tangent Function

6.6.3: Quadratic Functions

6.6.3.1: [RIT 214 - 214] Interprets zeros, extreme values, and symmetry of a graph within the context of a real-world quadratic relationship

Quadratics in Polynomial Form

6.6.3.3: [RIT 230 - 249] Describes the effects that changes in the constant terms have on the graphs of quadratic functions

Quadratics in Polynomial Form
Zap It! Game

6.6.3.4: [RIT 232 - 251] Evaluates a quadratic function for a given value in its domain

Quadratics in Factored Form
Quadratics in Polynomial Form

6.6.3.5: [RIT 234 - 254] Identifies the zeros of a polynomial function from a graph

Graphs of Polynomial Functions
Polynomials and Linear Factors

6.6.3.6: [RIT 239 - 255] Identifies the vertex, intercepts, or axis of symmetry of a quadratic function given a graph

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

6.6.3.8: [RIT 244 - 261] Determines the zeros of a quadratic function from a table of values

Quadratics in Polynomial Form
Quadratics in Vertex Form

6.6.3.9: [RIT 247 - 247] Writes the equation representing transformations of quadratic functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

Quadratics in Vertex Form
Translating and Scaling Functions

6.6.3.10: [RIT 247 - 280] Graphs quadratic functions

Quadratics in Polynomial Form
Quadratics in Vertex Form

6.6.3.11: [RIT 247 - 254] Evaluates a quadratic function for a given value in its domain to solve a real-world problem

Quadratics in Polynomial Form

6.6.3.12: [RIT 249 - 276] Graphs transformations of quadratic functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

Quadratics in Polynomial Form
Quadratics in Vertex Form

6.6.3.13: [RIT 250 - 266] Determines the maximum, minimum, y-intercept, or zeros of a quadratic function to solve real-world problems

Quadratics in Polynomial Form

6.6.3.14: [RIT 253 - 253] Recognizes the graph of a quadratic relationship

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

6.6.3.15: [RIT 254 - 279] Writes a quadratic function given the zeros

Quadratics in Factored Form
Quadratics in Polynomial Form

6.6.3.16: [RIT 254 - 275] Determines the vertex, intercepts, or axis of symmetry of a quadratic function given an equation

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

6.6.3.18: [RIT 259 - 259] Writes a quadratic function to represent real-world or mathematical contexts

Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic

6.6.3.19: [RIT 261 - 275] Determines an x-intercept of a quadratic function given the other x-intercept and the vertex or the axis of symmetry

Quadratics in Polynomial Form
Roots of a Quadratic

6.6.3.20: [RIT 262 - 289] Describes the effects that changes in the coefficients have on the graphs of quadratic functions

Quadratics in Polynomial Form
Roots of a Quadratic
Zap It! Game

6.6.3.21: [RIT 265 - 265] Understands the relationship between the zeros of a function and the x-intercepts of the graph of the function

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

6.6.3.22: [RIT 270 - 272] Writes a quadratic function given a graph

Quadratics in Factored Form

6.6.3.23: [RIT 272 - 277] Rewrites a quadratic equation into vertex form

Quadratics in Vertex Form

6.6.4: Exponential and Logarithmic Functions

6.6.4.1: [RIT 225 - 225] Interprets the meaning of the y-intercept of a graph within the context of a real-world exponential relationship

Exponential Growth and Decay

6.6.4.2: [RIT 234 - 255] Identifies the appropriate linear or exponential model that represents a real-world situation

Compound Interest
Exponential Functions
Exponential Growth and Decay
Slope-Intercept Form of a Line
Standard Form of a Line

6.6.4.3: [RIT 237 - 278] Understands that exponential models grow and decay by equal factors over equal intervals

Exponential Growth and Decay

6.6.4.4: [RIT 238 - 238] Describes the effects that changes in parameters have on the tables of values of exponential functions

Exponential Functions
Introduction to Exponential Functions

6.6.4.5: [RIT 240 - 264] Evaluates an exponential function for a given value in its domain to solve a real-world problem

Compound Interest
Exponential Functions
Exponential Growth and Decay

6.6.4.6: [RIT 241 - 277] Writes exponential functions to represent real-world or mathematical problems

Compound Interest
Exponential Growth and Decay
Introduction to Exponential Functions

6.6.4.7: [RIT 246 - 257] Classifies exponential functions as representations of growth or decay

Exponential Growth and Decay

6.6.4.8: [RIT 248 - 272] Describes the effects of changes in parameters on exponential functions that represent real-world relationships

Compound Interest
Exponential Growth and Decay

6.6.4.10: [RIT 252 - 264] Graphs an exponential function given a table of values

Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions

6.6.4.11: [RIT 254 - 261] Describes the effects that changes in parameters have on the graphs of exponential functions

Exponential Functions
Introduction to Exponential Functions

6.6.4.12: [RIT 256 - 278] Understands the relationship between the graphs of exponential and logarithmic functions

Logarithmic Functions

6.6.4.13: [RIT 259 - 270] Graphs exponential functions

Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions

6.6.4.14: [RIT 267 - 267] Writes an exponential function given a graph

Exponential Functions
Introduction to Exponential Functions

6.6.4.15: [RIT 267 - 274] Writes the equation representing transformations of exponential functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

Exponential Functions
Introduction to Exponential Functions

6.6.4.16: [RIT 270 - 270] Identifies the table of values given an exponential equation

Exponential Functions
Exponential Growth and Decay

6.6.4.17: [RIT 272 - 281] Applies the definition of logarithms to solve problems

Logarithmic Functions: Translating and Scaling

6.6.4.18: [RIT 275 - 275] Understands the exponential impact of the growth factor on values of an exponential function

Compound Interest
Exponential Growth and Decay

6.6.5: Piecewise/Absolute Value Functions

6.6.5.3: [RIT 249 - 276] Graphs absolute value functions

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

6.6.5.4: [RIT 250 - 250] Describes the effects of transformations on the graphs of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

Absolute Value with Linear Functions
Translating and Scaling Functions

6.6.5.5: [RIT 253 - 253] Determines the y-intercept of the transformation of an absolute value function, given the equation

Absolute Value with Linear Functions
Translating and Scaling Functions

6.6.5.6: [RIT 264 - 266] Writes the equation representing transformations of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

Translating and Scaling Functions

6.6.5.7: [RIT 269 - 269] Graphs transformations of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

6.6.5.8: [RIT 270 - 280] Graphs piecewise functions

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

6.6.5.9: [RIT 276 - 276] Writes a piecewise function given a graph

Translating and Scaling Functions

6.6.6: Rational Functions

6.6.6.1: [RIT 250 - 250] Evaluates a rational function for a given value in its domain

General Form of a Rational Function
Rational Functions

6.6.6.2: [RIT 251 - 291] Determines end behavior of rational functions

General Form of a Rational Function
Rational Functions

6.6.6.3: [RIT 253 - 253] Writes rational functions to represent real-world or mathematical problems

General Form of a Rational Function
Rational Functions

6.6.6.4: [RIT 260 - 265] Identifies the table of values that represents an inverse-variation relationship

Direct and Inverse Variation

6.6.6.5: [RIT 261 - 290] Determines x-intercepts for rational functions

General Form of a Rational Function

6.6.6.6: [RIT 261 - 281] Graphs rational functions

General Form of a Rational Function
Rational Functions

6.6.6.7: [RIT 268 - 268] Determines points of discontinuity for rational functions

General Form of a Rational Function

6.6.6.8: [RIT 269 - 269] Solves inverse variation problems

Direct and Inverse Variation

6.6.6.10: [RIT 288 - 288] Determines horizontal asymptotes for rational functions

General Form of a Rational Function
Rational Functions

6.6.7: Radical Functions

6.6.7.1: [RIT 278 - 278] Describes the effects of transformations on the graphs of radical functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

Radical Functions

6.7: Definitions, Properties, and Operations of Functions

6.7.1: Properties and Operations of Functions

6.7.1.1: [RIT 206 - 206] Expresses a relation defined by a mapping diagram as a set of ordered pairs

Introduction to Functions

6.7.1.2: [RIT 235 - 239] Determines the input of a function given an output

Function Machines 1 (Functions and Tables)

6.7.1.3: [RIT 238 - 263] Identifies the type of function by its equation

Absolute Value with Linear Functions
General Form of a Rational Function
Linear Functions
Logarithmic Functions
Radical Functions

6.7.1.4: [RIT 238 - 265] Performs operations with functions

Addition and Subtraction of Functions

6.7.1.7: [RIT 248 - 258] Distinguishes between linear and nonlinear functions given an equation, a graph, or a table of values

Graphs of Polynomial Functions

6.7.1.12: [RIT 263 - 270] Determines if a relation defined by a set of ordered pairs, a table of values, or a graph is a function

Introduction to Functions
Linear Functions

6.7.1.14: [RIT 264 - 280] Determines the domain of a rational function

Rational Functions

6.7.1.17: [RIT 276 - 288] Determines the domain of a logarithmic function

Logarithmic Functions

6.7.1.21: [RIT 283 - 289] Graphs the inverse of a function

Logarithmic Functions

6.7.1.23: [RIT 285 - 285] Describes properties of even or odd functions

Graphs of Polynomial Functions

Content correlation last revised: 9/27/2021