# 5: Functions

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## Learning Objectives

By the end of this chapter, the student should be able to

• Evaluate and define a function
• Identify the independent and dependent variable and their units
• Apply algebraic operations on functions
• Recognize the shape of a function’s graph with its name and formula

There are many different types of equations that we can work with in algebra because an equation gives the relationship between a variable(s) and numbers. For example,

$\dfrac{(x-3)^2}{9}-\dfrac{(y+2)^2}{4}=1\quad\text{or}\quad y=x^2-2x+7\quad\text{or}\quad\sqrt{y+x}-7=xy\nonumber$

all give relationships between variables and numbers. Some of these relationships are called functions.

## Definition: Function

A function is when one input of a relation is linked to only one output of the relation, i.e., a function has only one $$y$$ for one $$x$$.

Function notation is represented by $$f(x)$$ such that $f(x) = y,\nonumber$ and we say $$f$$ is a function of $$x$$.

This page titled 5: Functions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.