1. Relations and Functions
3-2
Relations and Functions
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1

2. Warm Up Generate ordered pairs for the function
y = x + 3 for x = –2, –1, 0, 1, and 2. Graph the ordered pairs.
(–2, 1)
(–1, 2)
(0, 3)
(1, 4)
(2, 5)
Holt McDougal Algebra 1

3. Objectives Define Relation and identify functions.
Find domain and range of relations and functions.
Holt McDougal Algebra 1

4. Vocabulary
relation
domain
range
function
Holt McDougal Algebra 1

5. Showing Multiple Representations of Relations
Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram.
x y
Table
Graph
Mapping Diagram x y 2 6 4 3 8 7 2 4 6 3 7 8
Holt McDougal Algebra 1

6. Finding the Domain and Range of a Relation
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 McDougal Algebra 1

7. x y Give the domain and range of the relation. Domain: {1, 4, 8} 1 4 8
Even though 1 is in the range twice, it is written only once when you are giving the range.
Holt McDougal Algebra 1

8. Give the domain and range of the relation.1 2 6 5 –4 –1
Domain: {6, 5, 2, 1}
Range: {–4, –1, 0}
Holt McDougal Algebra 1

9. Give the domain and range of the relation.
The domain value is all x-values from 1 through 5, inclusive.
Domain: 1 ≤ x ≤ 5
The range value is all y-values from 3 through 4, inclusive.
Range: 3 ≤ y ≤ 4
Holt McDougal Algebra 1

10. Identifying Functions
A function is a special type of relation that pairs each domain value with exactly one range value.
Holt McDougal Algebra 1

11. The relation is not a function. The domain value 3 is Repeated
Give the domain and range of the relation. Tell whether the relation is a function. Explain.
{(3, –2), (5, –1), (4, 0), (3, 1)}
D: {3, 5, 4}
Even though 3 is in the domain twice, it is written only once when you are giving the domain.
R: {–2, –1, 0, 1}
The relation is not a function.
The domain value 3 is Repeated
Holt McDougal Algebra 1

12. This relation is a function.
Give the domain and range of the relation. Tell whether the relation is a function. Explain. –4 2
Use the arrows to determine which domain values correspond to each range value. –8 1 4 5
D: {–4, –8, 4, 5}
R: {2, 1}
This relation is a function.
Each domain is paired with exactly one range value.
Holt McDougal Algebra 1

13. Draw lines to see the domain and range values.
Give the domain and range of the relation. Tell whether the relation is a function. Explain.
Draw lines to see the domain and range values.
Range
Domain
D: –5 ≤ x ≤ R: –2 ≤ y ≤ 1
The relation is not a function. It doesn’t pass the Vertical line Test.

14. Check It Out!
Give the domain and range of each relation. Tell whether the relation is a function and explain.
a. {(8, 2), (–4, 1), (–6, 2),(1, 9)} b.
Holt McDougal Algebra 1

15. Lesson Quiz: Part I
1. Express the relation {(–2, 5), (–1, 4), (1, 3), (2, 4)} as a table, as a graph, and as a mapping diagram.
Holt McDougal Algebra 1

16. 2. Give the domain and range of the relation.
Lesson Quiz: Part II
2. Give the domain and range of the relation.
D: –3 ≤ x ≤ 2: R: –2 ≤ y ≤ 4
Holt McDougal Algebra 1

17. The relation is not a function since 5 is paired with 2 and 4.
Lesson Quiz: Part III
3. Give the domain and range of the relation. Tell whether the relation is a function. Explain.
D: {5, 10, 15};
R: {2, 4, 6, 8};
The relation is not a function since 5 is paired with 2 and 4.
Holt McDougal Algebra 1