EXAMPLE 4 GRAPH AND .

EXAMPLE 5 GRAPH OR .

EXAMPLE 5 GRAPH AND .

DOMAIN & RANGE

EXAMPLE 1

Find the domain and range of the relation. {(5,12.8), (10, 16.2), (15,18.9), (20, 20.7), (25, 21.8)}

FUNCTIONS

MORE ON FUNCTIONS

A function (fnc) is a relation in which no two ordered pairs have the same first component and different second components.

Four Representations Verbally (in words) Numerically (table of values) Visually (a graph) Algebraically (a formula)

MAPPING – ILLUSTRATES HOW EACH MEMBER OF THE DOMAIN IS PAIRED WITH EACH MEMBER OF THE RANGE (NOTE: LIST DOMAIN AND RANGE VALUES ONCE EACH, IN ORDER.)

Draw a mapping for the following.

(5, 1), (7, 2), (4, -9), (0, 2)

0457

-912

Is this relation a function?

EXAMPLE 2

Determine whether each relation is a function and give the domain and range:

A) {(1,2), (3,4), (5,6), (5,8)}

B) {(1,2), (3,4), (6,5), (8,5)}

EXAMPLE 3

Determine if the given relation is a function and give the domain and range.

a) b)0 4

1 -1

2 4

3 7

4 -2

5 4

0 9

1 -1

1 4

2 7

3 -2

5 5

EXAMPLE 3 (CONT.)

0 9

1 -1

1 4

2 7

3 -2

5 5

THE VERTICAL LINE TEST

 

y

x

5

5

-5-5

y

x

5

5

-5-5

 

VERTICAL LINE TEST Graph the relation. (Use graphing

calculator or pencil and paper.)

Use the vertical line test to see if the relation is a function.

Vertical line test – If any vertical line passes through more than one point of the graph, the relation is not a function.

GRAPHICALLY IDENTIFYING THE DOMAIN & RANGE Your domain is the -values contained in

the graph. The -values contained in the graph are

your range. Write domain and range using interval

notation.

y

x

5

5

-5-5

y

x

5

5

-5-5

Example 4Determine if the graph is a function and state the domain and range.a) b)

Example 4 (cont.)c) d)

y

x

5

5

-5

-5

y

x

5

5

-5-5

Example 4 (cont.)e) f)

y

x

5

5

-5

-5

y

x

5

5

-5

-5

SECTION 3.6Function Notation and Linear Functions

EXAMPLE 1

Let and . Calculate . . . a.

b.

c.

d.

EXAMPLE 2

Let and . Calculate . . . a.

b.

EXAMPLE 2Use the graph to find the following.

a.

b.