# Chapter 3: A Picture is Worth a Thousand Words

**Advanced**Created by: CK-12

**Introduction**

In this chapter you will learn about linear functions. You will learn what is meant by a function, function notation and how to identify a function from a graph. You will also learn how to graph a linear function by creating a table of values and by plotting the \begin{align*}x\end{align*} and \begin{align*}y-\end{align*}intercepts. In addition, you will learn about the domain and the range of functions, what these terms mean, what proper notation is, and how to determine these from a graph.

The chapter will continue with graphing a quadratic function of the form \begin{align*}y = x^2\end{align*}. In this section, you will learn that a parabola has a vertex, an axis of symmetry, a domain and a range. You will also learn that a parabola can undergo transformations that will affect the vertex, the \begin{align*}y-\end{align*}values, the direction of the opening and its range. These transformations will be presented in the function as it is written in transformational form. At the end of the chapter, you will learn how to use these transformations to graph the function.

**Lessons**

In this chapter you will do the following lessons:

- Relation vs Function
- A Function
- Cartesian Graphs
- Graphing a linear function
- Domain and Range
- Graphing the Quadratic Function \begin{align*}y=x^2\end{align*}
- Transformations of \begin{align*}y=x^2\end{align*}
- Transformational form of \begin{align*}y=x^2\end{align*}

- 3.1.
## Relations vs Functions

- 3.2.
## Function Notation

- 3.3.
## The Many Points of the Cartesian Plane

- 3.4.
## Quiz I

- 3.5.
## Graphing a Linear Function Using a Table of Values

- 3.6.
## The Domain and Range of a Linear Function

- 3.7.
## Quiz II

- 3.8.
## Graphing the Quadratic Function y = x²

- 3.9.
## Transformations of y = x²

- 3.10.
## Transformational Form of y = x²

- 3.11.
## Chapter Test