College and Career Ready Standards

F.IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Absolute Value with Linear Functions

Exponential Functions

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Exponential Functions

Introduction to Functions

Linear Functions

Logarithmic Functions

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Standard Form of a Line

F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Absolute Value with Linear Functions

Translating and Scaling Functions

F.IF.3: Recognize patterns in order to write functions whose domain is a subset of the integers.

Arithmetic Sequences

Geometric Sequences

F.IF.4: For a function that models a relationship between two quantities, interpret key features of expressions, graphs and tables in terms of the quantities, and sketch graphs showing key features given a description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Roots of a Quadratic

Slope-Intercept Form of a Line

Translating and Scaling Sine and Cosine Functions

F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function

Introduction to Functions

Logarithmic Functions

Radical Functions

Rational Functions

F.IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Cat and Mouse (Modeling with Linear Systems)

Slope

F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.7a: Graph linear, quadratic and absolute value functions and show intercepts, maxima, minima and end behavior.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Graphs of Polynomial Functions

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

Slope-Intercept Form of a Line

Standard Form of a Line

Zap It! Game

F.IF.7b: Graph square root, cube root, and exponential functions.

Absolute Value with Linear Functions

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Radical Functions

Translating and Scaling Functions

F.IF.7c: Graph logarithmic functions, emphasizing the inverse relationship with exponentials and showing intercepts and end behavior.

Cosine Function

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

F.IF.7d: Graph piecewise-defined functions, including step functions.

Absolute Value with Linear Functions

Radical Functions

Translating and Scaling Functions

F.IF.7e: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Roots of a Quadratic

Zap It! Game

F.IF.7f: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function

Rational Functions

F.IF.7g: Graph trigonometric functions, showing period, midline, and amplitude.

Cosine Function

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

F.IF.8: Write a function in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8a: Use different forms of linear functions, such as slope-intercept, standard, and point-slope form to show rate of change and intercepts.

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

F.IF.8b: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Quadratics in Vertex Form

Roots of a Quadratic

F.IF.9: Compare properties of two functions using a variety of representations (algebraically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Quadratics in Polynomial Form

Quadratics in Vertex Form

F.BF.1: Use functions to model real-world relationships.

F.BF.1a: Combine multiple functions to model complex relationships.

Addition and Subtraction of Functions

F.BF.1b: Determine an explicit expression, a recursive function, or steps for calculation from a context.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

F.BF.1c: Compose functions.

Function Machines 1 (Functions and Tables)

F.BF.2: Write arithmetic and geometric sequences and series both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

F.BF.3: Transform parent functions (f(x)) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Quadratics in Vertex Form

Radical Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

F.BF.4: Find inverse functions.

F.BF.4b: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Function Machines 3 (Functions and Problem Solving)

Logarithmic Functions

F.BF.4c: Verify by composition that one function is the inverse of another.

F.BF.4d: Produce an invertible function from a non-invertible function by restricting the domain.

F.BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

F.LQE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LQE.1a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Compound Interest

Direct and Inverse Variation

Exponential Functions

Exponential Growth and Decay

Introduction to Exponential Functions

Linear Functions

Slope-Intercept Form of a Line

F.LQE.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Arithmetic Sequences

Compound Interest

Direct and Inverse Variation

Linear Functions

Slope-Intercept Form of a Line

F.LQE.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Compound Interest

Exponential Growth and Decay

F.LQE.2: Construct exponential functions, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Absolute Value with Linear Functions

Arithmetic Sequences

Arithmetic and Geometric Sequences

Compound Interest

Exponential Functions

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Geometric Sequences

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

F.TF.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Sine Function

Tangent Function

F.TF.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cosine Function

Sine Function

Tangent Function

F.TF.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4, and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi - x, pi + x, and 2pi - x in terms of their values for x, where x is any real number.

Cosine Function

Sine Function

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

F.TF.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

F.TF.8: Prove the Pythagorean identity sinĀ²(theta) + cosĀ²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant.

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

F.TF.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Sum and Difference Identities for Sine and Cosine

Correlation last revised: 9/15/2020