1. 7.2 Functions and Graphs Objective: Understand functions.
Fill out input-output tables.
Determine if relations are functions.

2. What is a function? We will use a machine as an example of a function.
Eli Whitney is famous for what invention?
The Cotton Gin!!

3. input x
domain
Function
(machine)
output y
range

4. Definition of Function
A function is a relation in which each element of the domain is paired with exactly one element of the range.

5. 4 ways to state relations
Ordered Pairs
Mapping
Graphs
Equations

6. Ordered Pairs (x, y)
In order for a relation of ordered pairs to be a function the domain must not repeat. For example {(5,5), (5, 6)} is a relation, but is not a function. because when you have 5 as the input the output is 5 or 6
{(6,-3), (4,1), (7, -2), (-3, 1)} Function?
{(1,2),(2, 3), (3, 4), (1, 3)} Function?

7. Mapping
A relation in map form is a function if there is only one arrow
coming from each element of the domain.
Domain
Range 1 2 4 6 2 4 6 8

8. Mapping
Is this relation a function?
Domain
Range 1 2 3 4 9 8 7 6

9. Mapping
Is this relation a function?
Domain
Range 1 2 3 4 5

10. Graphing Vertical Line Test (pencil test)
If you graph the order pairs from the relation, if you can touch a vertical line to more than one point on the graph then it is not a function.
Let’s go back and graph the ordered pairs and mapping examples and apply the vertical line test.

11. Input and Output TablesX
Domain
Output Y
Range -3 -2 -1 1 2 3
2x+1

12. Input and Output TablesX
Domain
Output Y
Range 4 2 5 3
-13
-3x + 2

13. The Vertical Line Test (aka The Pencil Test)
If a vertical line that passes through the graph of the function touches the graph in more than one place then the graph is NOT a function.
It is called the pencil test because most students use their pencil as a vertical line.
Hint: Vertical is up and down.

14. Assignment 7.2 Worksheet