Content Standards

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

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

Arithmetic Sequences

Geometric Sequences

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

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

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.

Introduction to Functions

Logarithmic Functions

Radical 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

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

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

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.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.

Modeling the Factorization of *x*^{2}+*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.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.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

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

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.

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

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

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

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.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

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.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.

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

Arithmetic Sequences

Compound Interest

Introduction to Exponential Functions

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

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

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

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

HS.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 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.

Sum and Difference Identities for Sine and Cosine

Correlation last revised: 1/22/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.