1: The student will demonstrate an understanding of the foundational properties and attributes of functions.

1.2A.1: The student uses properties and attributes of functions and applies functions to problem situations.

1.2A.1.A: identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations; and

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

1.2A.1.B: collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

Correlation
Real-Time Histogram
Solving Using Trend Lines

1.2A.4: The student connects algebraic and geometric representations of functions.

1.2A.4.A: identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x²), exponential (f(x) = a to the x power), and logarithmic (f(x) = logax) functions, absolute value of x(f(x) = |x|), square root of x (f(x) = square root of x), and reciprocal of x (f(x) = 1/x);

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Radical Functions
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B

1.2A.4.B: extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions; and

Cosine Function
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Parabolas - Activity A
Points, Lines, and Equations
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Roots of a Quadratic
Sine Function
Slope-Intercept Form of a Line - Activity B
Tangent Function
Translating and Scaling Functions

1.2A.4.C: describe and analyze the relationship between a function and its inverse.

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

2: The student will demonstrate an understanding of the use of representational tools to solve problems.

2.2A.2: The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

2.2A.2.A: use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations; and

Dividing Exponential Expressions
Exponents and Power Rules
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Translating and Scaling Functions

2.2A.2.B: use complex numbers to describe the solutions of quadratic equations.

Roots of a Quadratic

2.2A.3: The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations.

2.2A.3.A: analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;

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

2.2A.3.B: use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities; and

Modeling Linear Systems - Activity A
Points, Lines, and Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
System of Two Quadratic Inequalities
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

2.2A.3.C: interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

Modeling Linear Systems - Activity A
System of Two Quadratic Inequalities

3: The student will demonstrate an understanding of the properties of quadratic functions.

3.2A.6: The student understands that quadratic functions can be represented in different ways and translates among their various representations.

3.2A.6.A: determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

Parabolas - Activity A
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
System of Two Quadratic Inequalities

3.2A.6.B: relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; and

Cubic Function Activity
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Parabolas - Activity A
Points, Lines, and Equations
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

3.2A.6.C: determine a quadratic function from its roots (real and complex) or a graph.

Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

3.2A.8: The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

3.2A.8.A: analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

Parabolas - Activity A
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
System of Two Quadratic Inequalities

3.2A.8.B: analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

Roots of a Quadratic

3.2A.8.C: compare and translate between algebraic and graphical solutions of quadratic equations; and

Function Machines 2 (Functions, Tables, and Graphs)
Roots of a Quadratic

3.2A.8.D: solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

Factoring Special Products
Linear Inequalities in Two Variables - Activity A
Points, Lines, and Equations
Quadratic Inequalities - Activity A
Roots of a Quadratic
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
System of Two Quadratic Inequalities

4: The student will demonstrate an understanding of the connections between algebraic and geometric representations of quadratic functions and relations.

4.2A.5: The student knows the relationship between the geometric and algebraic descriptions of conic sections.

4.2A.5.A: describe a conic section as the intersection of a plane and a cone;

Parabolas - Activity A
Parabolas - Activity B
Surface and Lateral Area of Pyramids and Cones

4.2A.5.B: sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
Parabolas - Activity B
Quadratics in Factored Form
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions

4.2A.5.C: identify symmetries from graphs of conic sections;

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
Parabolas - Activity B
Quadratics in Factored Form

4.2A.5.D: identify the conic section from a given equation; and

Classifying Quadrilaterals - Activity B
Classifying Triangles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
Parallelogram Conditions
Special Quadrilaterals

4.2A.7: The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations.

4.2A.7.A: use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax² + bx + c and the y = a(x ? h)² + k symbolic representations of quadratic functions; and

Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

4.2A.7.B: use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x ? h)² + k form of a function in applied and purely mathematical situations.

Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions

5: The student will demonstrate an understanding of the properties of square root functions.

5.2A.9: The student formulates equations and inequalities based on square root functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

5.2A.9.A: use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;

Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Radical Functions
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions

5.2A.9.B: relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

Exponential Functions - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Functions Involving Square Roots
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Radical Functions

5.2A.9.C: determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

Functions Involving Square Roots
Radical Functions
Simplifying Radicals - Activity A
Simplifying Radicals - Activity B
Square Roots
System of Two Quadratic Inequalities

5.2A.9.D: determine solutions of square root equations using graphs, tables, and algebraic methods;

Points, Lines, and Equations

5.2A.9.E: determine solutions of square root inequalities using graphs and tables;

Linear Inequalities in Two Variables - Activity A
Square Roots
System of Two Quadratic Inequalities

5.2A.9.F: analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems; and

Functions Involving Square Roots
Radical Functions
Simplifying Radicals - Activity A
Simplifying Radicals - Activity B
System of Two Quadratic Inequalities

5.2A.9.G: connect inverses of square root functions with quadratic functions.

Functions Involving Square Roots
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Roots of a Quadratic

6: The student will demonstrate an understanding of the properties of rational functions.

6.2A.10: The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

6.2A.10.A: use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

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

6.2A.10.B: analyze various representations of rational functions with respect to problem situations;

General Form of a Rational Function
Rational Functions

6.2A.10.C: determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

General Form of a Rational Function
Rational Functions
System of Two Quadratic Inequalities

6.2A.10.D: determine the solutions of rational equations using graphs, tables, and algebraic methods;

Points, Lines, and Equations

6.2A.10.E: determine solutions of rational inequalities using graphs and tables;

Arithmetic Sequences
Points, Lines, and Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

6.2A.10.F: analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem; and

General Form of a Rational Function
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B
System of Two Quadratic Inequalities

6.2A.10.G: use functions to model and make predictions in problem situations involving direct and inverse variation.

Direct Variation
Direct and Inverse Variation
General Form of a Rational Function
Modeling Linear Systems - Activity A
Rational Functions
Road Trip (Problem Solving)

7: The student will demonstrate an understanding of the properties of exponential and logarithmic functions.

7.2A.11: The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

7.2A.11.A: develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Function Machines 3 (Functions and Problem Solving)

7.2A.11.B: use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Slope-Intercept Form of a Line - Activity B

7.2A.11.C: determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
System of Two Quadratic Inequalities

7.2A.11.D: determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

Exponential Functions - Activity A
Logarithmic Functions - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

7.2A.11.E: determine solutions of exponential and logarithmic inequalities using graphs and tables; and

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
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

7.2A.11.F: analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
System of Two Quadratic Inequalities