HS.F-IF: Interpreting Functions

1.1: Understand the concept of a function and use function notation

HS.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

HS.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

HS.F-IF.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic Sequences
Geometric Sequences

1.2: Interpret functions that arise in applications in terms of the context

HS.F-IF.4: Use tables, graphs, verbal descriptions, and equations to interpret and sketch the key features of a function modeling the relationship between two quantities.

Absolute Value with Linear Functions
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

HS.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

HS.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

1.3: Analyze functions using different representations

HS.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.

HS.F-IF.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima where appropriate.

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

HS.F-IF.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions
Translating and Scaling Functions

HS.F-IF.7.c: 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

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

General Form of a Rational Function
Rational Functions

HS.F-IF.7.e: Graph exponential and logarithmic functions, 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

HS.F-IF.7.f: Graph f(x) = sin x and f(x) = cos x as representations of periodic phenomena.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

HS.F-IF.7.g: Graph trigonometric functions, showing period, midline, phase shift and amplitude.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

HS.F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

HS.F-IF.8.a: 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 ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic

HS.F-IF.8.b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest
Exponential Functions

HS.F-IF.9: Compare properties of two functions each represented in a different way (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

HS.F-BF: Building Functions

2.1: Build a function that models a relationship between two quantities

HS.F-BF.1: Write a function that describes a relationship between two quantities.

HS.F-BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

HS.F-BF.1.b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

HS.F-BF.1.c: Compose functions.

Function Machines 1 (Functions and Tables)

HS.F-BF.2.i: Write arithmetic and geometric sequences both recursively and with an explicit formula and convert between the two forms.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

HS.F-BF.2.ii: Use sequences to model situations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

2.2: Build new functions from existing functions

HS.F-BF.3.i: Identify the effect on the graph of replacing f(x) by f(x) + k, f(x + k), kf(x), and f(kx), for specific values of k (both positive and negative); find the value of k given the graphs.

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

2.2.1.1: Technology may be used to experiment with the effects of transformations on a graph.

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

HS.F-BF.4: Find inverse functions.

HS.F-BF.4.a: Write an equation for the inverse given a function has an inverse.

Logarithmic Functions

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

Logarithmic Functions

HS.F-BF.4.c: 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

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

Logarithmic Functions

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

Logarithmic Functions

HS.F-LE: Linear, Quadratic, and Exponential Models

3.1: Construct and compare linear, quadratic, and exponential models and solve problems

HS.F-LE.1.i: Identify situations that can be modeled with linear, quadratic, and exponential functions.

Absolute Value with Linear Functions
Arithmetic Sequences
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Quadratics in Polynomial Form
Slope-Intercept Form of a Line

HS.F-LE.1.ii: Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays.

Arithmetic Sequences
Compound Interest
Direct and Inverse Variation
Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions
Linear Functions
Slope-Intercept Form of a Line

HS.F-LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description, or two input-output pairs given their relationship.

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

HS.F-LE.3: Compare the end behavior of linear, quadratic, and exponential functions using graphs and/or tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing as a linear or quadratic function.

Compound Interest
Introduction to Exponential Functions

HS.F-LE.4: Use logarithms to express the solution to ab to the ct power = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

Compound Interest
Logarithmic Functions

3.2: Interpret expressions for functions in terms of the situation they model

HS.F-LE.5: Interpret the parameters in a linear, quadratic, or exponential function in context.

Arithmetic Sequences
Compound Interest
Exponential Growth and Decay
Introduction to Exponential Functions

HS.F-TF: Trigonometric Functions

4.1: Extend the domain of trigonometric functions using the unit circle

HS.F-TF.1: Understand that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.

Sine Function
Tangent Function

HS.F-TF.2.ii: 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

HS.F-TF.3.i: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6.

Cosine Function
Sine Function
Sum and Difference Identities for Sine and Cosine
Tangent Function
Translating and Scaling Sine and Cosine Functions

HS.F-TF.3.ii: 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

HS.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

4.2: Model periodic phenomena with trigonometric functions

HS.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

4.3: Prove and apply trigonometric identities

HS.F-TF.8: Prove the Pythagorean identity sin² (theta) + cos² (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 of the angle.

Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios

HS.F-TF.9: Know and apply the addition and subtraction formulas for sine, cosine, and tangent.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine