1. Essential Question The student will be able to:
How do I determine if a relation is a function and how do I find the value of a function.
Priority Standard: 8 F 1
Adapted by Christopher Carnes, Rancho Viejo Middle School

2. Relations
A relation is a mapping, or pairing, of input values with output values.
The set of input values is called the Domain
The set of output values is called the Range

3. Domain is the set of all X values
List in order from smallest to largest
Do not duplicate any values

4. Range is the set of all Y values
List in order from smallest to largest
Do not duplicate any values

5. Examples

6. Functions
A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x).
f(x) y x

7. Function Notation
Input
Name of Function
Output

8. Determine whether each relation is a function.
1. {(2, 3), (3, 0), (5, 2), (4, 3)}
YES, every domain is different!
f(x) 2 3
f(x) 3
f(x) 5 2
f(x) 4 3

9. Determine whether the relation is a function.
2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
f(x) 4 1
f(x) 5 2
NO, 5 is paired with 2 numbers!
f(x) 5 3
f(x) 6
f(x) 1 9

10. Is this relation a function? {(1,3), (2,3), (3,3)}
Yes No
Answer Now

11. 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!

12. Vertical Line Test
FUNCTION!
NO!
NO WAY!
FUNCTION!

13. Is this a graph of a function?
Yes No
Answer Now

14. 3(3)-2 3 7 -2 -8 3(-2)-2 Given f(x) = 3x - 2, find: 1) f(3) = 7
= -8
3(-2)-2 -2 -8

15. Given h(z) = z2 - 4z + 9, find h(-3)
(-3)2-4(-3)+9 -3 30
h(-3) = 30

16. Given g(x) = x2 – 2, find g(4) 2 6 14 18
Answer Now

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