Academic standards list

High School: Functions — Mathematics


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

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.
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal

Building Functions

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
Find inverse functions.
     There are 4 components within this standard.
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and

Linear, Quadratic, and Exponential Models

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
Interpret the parameters in a linear or exponential function in terms of a context.

Trigonometric Functions

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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