1. Objective
SWBAT use graphs to represent relations and functions

2. Section 8.1 “Relations and Functions”
Age (years), x 2 4 5 7
Length (in.), y 32 59 65 69 96
The relationship between age and length can be
represented using ordered pairs.
(2, 32), (4, 59), (5, 65), (5, 69), (7, 96)
The ordered pairs form a RELATION.
RELATION
a pairing of numbers from one set, called the DOMAIN, with the numbers in another set, called the RANGE.

3. RELATION- DOMAIN contains numbers called INPUTS
Consists of the following:
DOMAIN contains numbers called
INPUTS
RANGE contains numbers called
OUTPUTS
The INPUTS are the X-coordinates and the OUTPUTS are the Y-coordinates.

4. RELATION Set 1 Set 2 Domain Range Input Output X-coordinate
a pairing of numbers from one set, called the DOMAIN, with the numbers in another set, called the RANGE.
Set 1
Set 2
Domain
Range
Input
Output
X-coordinate
Y-coordinate

5. RELATION x 2 4 6 8 y 1 3
In addition to using ordered pairs or a table to represent a relation, you can also use a GRAPH or a MAPPING DIAGRAM.
MAPPING DIAGRAM
GRAPH
Input
Output

6. Represent the relation as a graph and mapping diagram.
(1,10), (2, 15), (3, 10), (3, 20), (4, 25)
MAPPING DIAGRAM
GRAPH
Input
Output 1 2 3 4 10 15 20 25

7. The domain is the set of inputs: 10, 12, 13,
Identify the domain and range of a relation
The input-output table shows the cost of various amounts of regular unleaded gas from the same pump. Identify the domain and range of the relation. 10
Input gallons
Output dollars 12 13 17
19.99
23.99
25.99
33.98
19.99, 23.99, 25.99, and
The domain is the set of inputs:
10, 12, 13,
and 17.The
range is the set of outputs:

8. Each input must be paired with only ONE output
FUNCTION-
Is a relation in which for each input there is EXACTLY ONE output.
FUNCTION
NOT A FUNCTION
3 5
Each input must be paired with only ONE output

9. FUNCTION-
Is a relation in which for each input there is EXACTLY ONE output.
FUNCTION
NOT A FUNCTION
When a relation is represented as a graph, you can use the VERTICAL LINE TEST. If you can draw a vertical line through any two points on the graph, then the relation is NOT a function.

10. “To Be or Not To Be” a FUNCTION1 2
Output 12 9 6 3
Input 3 2 1
Output 7 4
Input
FUNCTION
NOT A FUNCTION
2 4 7
The pairing is a function because each input is paired with exactly one output.
The pairing is not a function because each input is
not paired with exactly one output.

11. DO NOW
Pg. 387 Guided Practice
Problems 1-7

12. Homework
Text p. 388, #8-22 evens and #19