# Academic standards list

### High School: Functions — Mathematics

### Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

### Interpreting Functions

CCSS.Math.Content.HSF-IF

Understand the concept of a function and use function notation

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…

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

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci…

Interpret functions that arise in applications in terms of the context

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and…

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function…

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the…

Analyze functions using different representations

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

*There are 5 components within this standard*.Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

*There are 2 components within this standard*.### Building Functions

CCSS.Math.Content.HSF-BF

Build a function that models a relationship between two quantities

Write a function that describes a relationship between two quantities.*

*There are 3 components within this standard*.Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the…

Build new functions from existing functions

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and…

### Linear, Quadratic, and Exponential Models

CCSS.Math.Content.HSF-LE

Construct and compare linear and exponential models and solve problems

Distinguish between situations that can be modeled with linear functions and with exponential functions.

*There are 3 components within this standard*.Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two…

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or…

For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the…

Interpret expressions for functions in terms of the situation they model

### Trigonometric Functions

CCSS.Math.Content.HSF-TF

Extend the domain of trigonometric functions using the unit circle

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

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian…

(+) 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…

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Model periodic phenomena with trigonometric functions

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to…

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and…

Prove and apply trigonometric identities

Prove the Pythagorean identity sin2() + cos2() = 1 and use it to find sin(), cos(), or tan() given sin(), cos(), or tan() and the quadrant of…

(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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