Holt Algebra 1

4-2 Relations and Functions

Warm Up

Generate ordered pairs for the function

y = x + 3 for x = –2, –1, 0, 1, and 2.

Find the y values, and put them together as an ordered pairs as (x,y)

(–2, 1)

(–1, 2)

(0, 3)

(1, 4)

(2, 5)

x y (x,y)

-2

-1

0

1

2

1

2

3

4

5

y = x + 3 =-2 + 3 = 1

y = x + 3 = -1 + 3 = 2

y = x + 3 = 0 + 3 = 3

y = x + 3 = 1 + 3 = 4

y = x + 3 = 2 + 3 = 5

Holt Algebra 1

4-2 Relations and Functions

Identify functions.

Find the domain and range of relations and functions.

Objectives

Holt Algebra 1

4-2 Relations and Functions

Showing Multiple

Representations of Relations

Example 1:

Express the relation {(2, 3), (4, 7), (6, 8)}:

1. as a table,

2. as a graph,

3. and as a mapping diagram.

Holt Algebra 1

4-2 Relations and Functions

1. Represent as Table:

{(2, 3), (4, 7), (6, 8)}

Write all x-values under “x”

2

4

6

3

7

8

x y

Table

x x x

and write all y-values under “y”.

y y y

Holt Algebra 1

4-2 Relations and Functions

{(2, 3), (4, 7), (6, 8)}

Use the x- and y-values to

plot the ordered pairs.

Graph

2. Represent as Graph:

(2,3)

(4,7) (6,8)

Holt Algebra 1

4-2 Relations and Functions

2

6

4

3

8

7

Mapping Diagram

x y Write all x-values under “x” and all y-values under “y”. Draw an

arrow from each x-value to its corresponding y-value.

{(2, 3), (4, 7), (6, 8)}

3. Represent as Mapping Diagram:

Holt Algebra 1

4-2 Relations and Functions

Your turn to try it!!! PRACTICES

Express the relation {(1, 3), (2, 4), (3, 5)} as a table, as a graph, and as a mapping diagram.

x y

1 3

2 4

3 5

Table Graph

1

2

3

3

4

5

Mapping Diagram

x y

Holt Algebra 1

4-2 Relations and Functions

The domain of a relation is the set of first coordinates (or x-values) of the ordered pairs.

The range of a relation is the set of second coordinates (or y-values) of the ordered pairs.

Holt Algebra 1

4-2 Relations and Functions

my EX WIFE is a DR.

X Domain

Remember this way:

y Range

Holt Algebra 1

4-2 Relations and Functions

Check It Out! Example 2a

Give the domain and range of the relation.

–4

–1

0 1

2

6

5 Domain: {6, 5, 2, 1}

Range: {–4, –1, 0}

Holt Algebra 1

4-2 Relations and Functions

Check It Out! Example 2b

Give the domain and range of the relation.

x y

1 1

4 4

8 1

Domain: {1, 4, 8}

Range: {1, 4}

Holt Algebra 1

4-2 Relations and Functions

A function is a special type of relation that pairs each domain value with exactly one range value.

Notes:

If it is a function, then none of x (domain) value should be repeated

Holt Algebra 1

4-2 Relations and Functions

Example 3A: Identifying Functions

Give the domain and range of the relation. Tell whether the relation is a function. Explain.

{(3, –2), (5, –1), (4, 0), (3, 1)}

The relation is not a function. Each domain value does not have exactly one range value.

The domain value 3 is repeated, paired with the range values –2 and 1.

Holt Algebra 1

4-2 Relations and Functions

–4

–8

4

2

1

5

{(-4, 2), (-8, 2), (4, 1), (5, 1)}

This relation is a function. Each domain value is paired with exactly one range value.

Example 3B: Identifying Functions

Give the domain and range of the relation. Tell whether the relation is a function. Explain.

Holt Algebra 1

4-2 Relations and Functions

Example 3C: Identifying Functions Give the domain and range of the relation. Tell whether the relation is a function. Explain.

Draw in lines to see

the domain and range

values

The relation is not a function. Nearly all domain values have more than one range value.

(-3,1)

(-3,-2)

Check out the points

that the line cut

through the plane