1. Functions and Relations
Pg. 57 – 58

2. Do Now
Create a mapping to organize the following ordered pairs: (9, 3), (2, -1), (8, 3) (-4, 0), (0, 0) What is the domain? What is the range?

3. Functions
A function is a relation in which each element of the domain is paired with exactly one element of the range.
If the x value repeats, then a relation is NOT a function.
f(x) y x

4. Function Notation
Input
Name of Function
Output

5. Vertical Line Test (pencil test)
If any vertical line passes through more than one point of the graph, then that relation is not a function.
Are these functions?
FUNCTION!
FUNCTION!
NOPE!

6. Is this relation a function?
Class Example 1
Is this relation a function?
{(2, 3), (3, 0), (5, 2), (4, 3)}

7. Class Example 2
FUNCTION!
NO!
NO WAY!
FUNCTION!

8. Class Example 3 Given f(x) = 3x - 2, find:
= 7
3(3)-2 3 7
= -8
3(-2)-2 -2 -8

9. Class Example 4 Given g(x) = x2 – 2
If the domain is {-2, 0, 5}, what is the range?

10. Class Example 5 Given g(x) = 2x + 1
If the domain is {-2, 0, 5}, what is the range? If the range is {-5, -1, 3}, what is the domain?

11. Is this relation a function? {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
Student Example 1
Is this relation a function?
{(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}

12. Is this a graph of a function?
Student Example 2
Is this a graph of a function?

13. Student Example 3 Given h(x) = x2 – 4x + 9, find h(-3)
(-3)2-4(-3)+9 30 -3
h(-3) = 30

14. Student Example 4 Is this relation a function? {(1,3), (2,3), (3,3)}

15. Student Example 5
-40
-25 -5 10
Answer Now

16. Classwork Bonus!! Given f(x) = 2x + 1, find -4[f(3) – f(1)]
-40
-16 -8 4
Answer Now