# Functions

Contents
Functions are mathematical entities that assign unique outputs to given inputs. Sounds simple? Think again! In this topic you will evaluate, graph, analyze, and create various types of functions.

## Introduction to functions

Make a first introduction to functions.

## Evaluating functions

Learn how to find the value of a function for a given input value.

## Inputs and outputs of a function

Extend your understanding of the relationship between the inputs of a function and the outputs of that function.

## Functions and equations

Understand the subtle differences and similarities between functions and equations. In this exercise, we will see how an equation can be turned into a function.

## Interpreting function notation

Solve some word problems by interpreting expressions of modeling functions.

## Introduction to the domain and range of a function

Learn what the domain and the range of a function are. Practice finding the domain and the range of a function given its graph.

## Determining the domain of a function

Determine the domains of functions according to various considerations.

## Recognizing functions

Learn how to distinguish between two-variable relationships that are functions and two-variable relationships that aren't functions.

## Piecewise functions

Piecewise functions are functions that have different assignment rules for different numbers. For example, a function can return x² for any negative x-value and return x³ for any non-negative x-value.

## Maximum and minimum points

Learn about maximum and minimum points of functions.

## Intervals where a function is positive, negative, increasing, or decreasing

Learn about features of functions that have distinct graphical representations: intervals where the function is always positive or always negative, and intervals where the function is always increasing or always decreasing.

## Interpreting features of graphs

Interpret the graphs of functions in terms of the contexts that are modeled by the functions.

## Average rate of change

Learn what's the average rate of change of a function and how to find it over given intervals.

## Average rate of change word problems

Solve word problems that concern the average rate of change of a functional relationship.