1. I can determine whether a relation is a function
2.5A: What is a function?
I can determine whether a relation is a function

2. f x y x y Recall… input output Definition of a function:
Each ____is paired with only one ____ x y
input
x is called the _________
y is called the _________
Each input gives its own output
output x y f
Function Machine

3. Example 1 When each element in the domain (x) is paired
When we graph f(x) = x + 2, is it a function? How can we tell? x y -2 -1 1 2 1 2
When each element in the domain (x) is paired
with one element in the range (y) 3 4

4. Vertical Line Test (VLT)
This is a function – a vertical line only
hits the graph once
This is a NOT a function – a vertical line
hits the graph more than once

5. Does this graph pass the VLT?

6. Does this graph pass the VLT?

7. Does this graph pass the VLT?

8. YES! YES! Mappings: Example 2 -1 1 2 2 3 4 5 -1 1 2 2 x y -1 2 3 1 4 53 1 4 5 -1 1 2 2 3 4 5
Is this a function?
YES! x y -1 2 1 -1 1 2
Is this a function? 2
YES!

9. NO! It is a function if each ‘x’ gets mapped to ONLY ONE ‘y’ -1 2 2 33 4 5 -1 2 2 3 4 5
Is this a function?
NO!

10. A. B. Are you a master? (1, 3) (2, 5) (1, -8)
Which of the following are functions? A. B.
(1, 3) (2, 5) (1, -8)

11. C. D. Are you a master? 3 6 4 8 Which of the following are relations?x y 3 6 4 7 8 3 6 8 4