### 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).

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.

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

#### 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.

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

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.

#### 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.

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

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

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

HS.F-IF.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior.

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

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

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.

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

### 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.

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

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

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

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

#### 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.

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

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.b: Verify by composition that one function is the inverse of another.

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: 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.

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.

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.

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.

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.

#### 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.

### 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.

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.

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.

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.

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

#### 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.

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

Correlation last revised: 9/22/2020

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