1: The student uses mathematical processes to acquire and demonstrate mathematical understanding.

1.A: apply mathematics to problems arising in everyday life, society, and the workplace;

Estimating Population Size

1.B: use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

Estimating Population Size

2: The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.

2.A: graph the functions f(x)=?x, f(x)=1/x, f(x)=x³, f(x)= ³?x, f(x)=b to the x power, f(x)=|x|, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval;

Cubic Function Activity
Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
General Form of a Rational Function
Holiday Snowflake Designer
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Radical Functions
Rational Functions

2.C: describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range; and

Exponential Functions - Activity A
Functions Involving Square Roots
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratics in Factored Form
Radical Functions
Roots of a Quadratic

2.D: use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.

Function Machines 3 (Functions and Problem Solving)

3: The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions.

3.B: solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution;

Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

3.E: formulate systems of at least two linear inequalities in two variables;

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
System of Two Quadratic Inequalities
Systems of Linear Inequalities (Slope-intercept form) - Activity A

3.F: solve systems of two or more linear inequalities in two variables; and

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
System of Two Quadratic Inequalities
Systems of Linear Inequalities (Slope-intercept form) - Activity A

3.G: determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.

System of Two Quadratic Inequalities
Systems of Linear Inequalities (Slope-intercept form) - Activity A

4: The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.

4.A: write the quadratic function given three specified points in the plane;

Quadratics in Factored Form
Roots of a Quadratic

4.B: write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening;

Parabolas - Activity A

4.C: determine the effect on the graph of f(x) = ?x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d;

Addition and Subtraction of Polynomials
Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Parabolas - Activity A
Points, Lines, and Equations
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions

4.D: transform a quadratic function f(x) = ax² + bx + c to the form f(x) = a(x - h)² + k to identify the different attributes of f(x);

Quadratics in Factored Form
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions

4.E: formulate quadratic and square root equations using technology given a table of data;

Functions Involving Square Roots
Radical Functions

4.F: solve quadratic and square root equations;

Functions Involving Square Roots
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Radical Functions
Roots of a Quadratic

4.G: identify extraneous solutions of square root equations; and

Functions Involving Square Roots
Radical Functions

4.H: solve quadratic inequalities.

Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
System of Two Quadratic Inequalities

5: The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.

5.A: determine the effects on the key attributes on the graphs of f(x) = b to the x power and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d;

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Slope-Intercept Form of a Line - Activity B

6: The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.

6.A: analyze the effect on the graphs of f(x) = x³ and f(x) = ³?x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d;

Addition and Subtraction of Polynomials
Cubic Function Activity
Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Parabolas - Activity A
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions

6.B: solve cube root equations that have real roots;

Cubic Function Activity
Modeling and Solving Two-Step Equations
Polynomials and Linear Factors
Solving Two-Step Equations

6.C: analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;

Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Points, Lines, and Equations
Quadratic and Absolute Value Functions
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions

6.F: solve absolute value linear inequalities;

Inequalities Involving Absolute Values
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

6.G: analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;

Function Machines 2 (Functions, Tables, and Graphs)
General Form of a Rational Function
Rational Functions
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions

6.K: determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation; and

General Form of a Rational Function
Rational Functions

6.L: formulate and solve equations involving inverse variation.

Direct and Inverse Variation
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

7: The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.

7.B: add, subtract, and multiply polynomials;

Addition of Polynomials - Activity A

7.C: determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two;

Dividing Polynomials Using Synthetic Division

7.D: determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods;

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

7.E: determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping;

Cubic Function Activity
Factoring Special Products
Modeling the Factorization of x²+bx+c

7.F: determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two;

Dividing Exponential Expressions
Exponents and Power Rules

7.G: rewrite radical expressions that contain variables to equivalent forms;

Simplifying Radical Expressions - Activity A
Simplifying Radical Expressions - Activity B

7.H: solve equations involving rational exponents; and

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

7.I: write the domain and range of a function in interval notation, inequalities, and set notation.

Functions Involving Square Roots

8: The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions.

8.A: analyze data to select the appropriate model from among linear, quadratic, and exponential models;

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B

8.B: use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data; and

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratics in Factored Form
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B

8.C: predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratics in Factored Form
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B