Easy Algebra Step-by-Step

Basic Function Concepts 201

Form 3: Graphical Representation

An additional way to represent a function is by graphing the function in the

Cartesian coordinate plane. You can easily determine whether a graph is

the graph of a function by using the vertical line test. A graph is the graph

of a function if and only if no vertical line crosses the graph in more than

one point. This is a quick visual determination and is the graphical

equivalent of saying that no two different ordered pairs have the same fi rst

coordinate.

Problem Determine which of the following is the graph of a function.

4

2

a. b. c.

y

x

2

–2

y

x

2

–2

y

x

Solution

Step 1. Mentally apply the vertical line test to each graph.

a. This is the graph of a function.

b. This is not the graph of a function because a vertical line drawn through

the point x = 1 will cross the graph in more than one point. (Actually, there

are infi nitely many vertical lines that will cross in more than one point, but

it only takes one to ascertain it is not a function.)

c. This is the graph of a function.

Some Common Functions

Some of the more common functions you will study in algebra are listed

here in general form and given special names.

a. y = f(x) = ax + b Linear function

b. y = f(x) = ax^2 + bx + c, a ≠ 0 Quadratic function