Growth: Grades 6+ Math - Algebraic Concepts (2017) Gizmos | Browse by Core Curriculum

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6.1.2.34: [RIT 232 - 238] Recognizes arithmetic sequences

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6.2.1.17: [RIT 239 - 261] Factors quadratic trinomials

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

6.2.1.19: [RIT 239 - 257] Multiplies monomials

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

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

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

6.2.1.24: [RIT 244 - 273] Simplifies rational expressions

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

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

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

6.2.1.33: [RIT 256 - 263] Multiplies polynomials

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

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

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

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

6.2.1.40: [RIT 265 - 270] Squares binomial expressions

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

6.2.2: Numerical Expressions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6.2.3: Exponents

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6.3.1.13: [RIT 238 - 243] Writes an inequality in the form x > c or x

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

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

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

6.3.1.18: [RIT 243 - 243] Represents an inequality in the form x > c or x

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

6.3.1.20: [RIT 244 - 251] Writes an inequality in the form x > c or x

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

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

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

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

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

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

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

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

6.3.1.31: [RIT 263 - 263] Solves quadratic inequalities

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6.3.2.61: [RIT 257 - 257] Solves polynomial equations

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6.5.2: Linear Functions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6.6: Nonlinear Functions

6.6.1: Polynomial Functions

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

6.6.1.3: [RIT 267 - 267] Evaluates a polynomial function 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

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

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

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

6.6.2: Trigonometric Functions/Radian Measure

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

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

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

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

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

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

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

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

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

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

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

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

6.6.3.10: [RIT 247 - 280] Graphs quadratic functions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6.6.4.13: [RIT 259 - 270] Graphs exponential functions

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

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

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

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

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

6.6.5: Piecewise/Absolute Value Functions

6.6.5.3: [RIT 249 - 276] Graphs absolute value 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

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

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

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

6.6.5.8: [RIT 270 - 280] Graphs piecewise functions

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

6.6.6: Rational Functions

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

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

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

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

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

6.6.6.6: [RIT 261 - 281] Graphs rational functions

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

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

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

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

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

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

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

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

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

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

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

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

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