Relations And Functions

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) x

y

(x,y)

-2

1

(–2, 1)

y=x+3

=-2 + 3

=1

-1

2

(–1, 2)

y=x+3

= -1 + 3

=2

0

3

(0, 3)

y=x+3

=0+3

=3

1

4

(1, 4)

y=x+3

=1+3

=4

2

5

(2, 5)

y=x+3

=2+3

=5

Holt Algebra 1

4-2 Relations and Functions

Objectives Identify functions. Find the domain and range of relations and functions.

Holt Algebra 1

4-2 Relations and Functions

Sho wing Mul ti ple Re pre sen tat io ns o f Re la tio ns 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. Rep res en t as Tab le : x y

x y

x

y

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

x

y

2

3

4

7

6

8

Holt Algebra 1

Write all x-values under “x” and write all y-values under “y”.

4-2 Relations and Functions

2. Rep res en t as Graph : {(2, 3), (4, 7), (6, 8)} Graph (4,7)

(2,3)

Holt Algebra 1

(6,8)

Use the x- and y-values to plot the ordered pairs.

4-2 Relations and Functions

3. Rep res en t as Ma pp ing Dia gram: {(2, 3), (4, 7), (6, 8)}

Mapping Diagram

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x

y

2

3

4

7

6

8

Write all x-values under “x” and all y-values under “y”. Draw an arrow from each x-value to its corresponding y-value.

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. Table

Graph

Mapping Diagram y x

x

y

1

3

1

3

2

4

2

4

3

5

3

5

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

Remember this way: y

Range

my EX WIFE is a DR. X

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Domain

4-2 Relations and Functions Check It Out! Example 2a Give the domain and range of the relation. 6 5 2 1

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–4 –1 0

Domain: {6, 5, 2, 1} Range: {–4, –1, 0}

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

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Domain: {1, 4, 8} Range: {1, 4}

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 Example 3B: Identifying Functions Give the domain and range of the relation. Tell whether the relation is a function. Explain. –4 –8 4 5

2

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

1

This relation is a function. Each domain value is paired with exactly one range value. 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. (-3,1) (-3,-2)

Draw in lines to see the domain and range values Check out the points that the line cut through the plane

The relation is not a function. Nearly all domain values have more than one range value. Holt Algebra 1