Sullivan Algebra & Trigonometry: Section 3.2The Graph of a Function

Objectives

• Identify the Graph of a Function

• Obtain Information from or about the Graph of a Function

When a function is defined by an equation in x and y, the graph of the function is the graph of the equation, that is, the set of all points (x,y) in the xy-plane that satisfies the equation.

Vertical Line Test for Functions:

A set of points in the xy-plane is the graph of a function if and only if a vertical line intersects the graph in at most one point.

x

y

Example: Does the following graph represent a function?

The graph does not represent a function, since it does not pass the vertical line test.

Example: Does the following graph represent a function?

The graph does represent a function, since it does pass the vertical line test.

x

y

The graph of f(x) is given below.

4

0

-4(0, -3)

(2, 3)

(4, 0) (10, 0)

(1, 0) x

y

What is the domain and range of f ?

Domain: [0,10]

Range: [-3,3]

Find f(0), f(4), and f(12)

f(0) = -3

f(4) = 0

f(12) does not exist since 12 isn’t in the domain of f

Does the graph represent a function?

4

0

-4

(0, -3)

(2, 3)

(4, 0)

(10, -3)

(1, 0) x

y

(7, -3)

Yes

For which x is f(x)=0?

4

0

-4(0, -3)

(2, 3)

(4, 0)

(10, -3)

(1, 0) x

y

(7, -3)