1. Introduction to Functions

2. A relation can be displayed in 4 ways:
A relation is a set of ordered pairs
A relation can be displayed in 4 ways:
{(4,1),(-7,3),(8,2),(0,3)} X Y 3 8 -2 4 6 1 -3 7 -3 2 8 4 1

3. The range is the set of y-values
Domain
The domain is the set of x-values
Range
The range is the set of y-values
Braces { } are used when you write a set
Write the numbers from least to greatest
Do not repeat numbers

4. 7 -3 2 8 4 1
{(4,1),(-7,3),(8,2),(0,3)} X Y 3 8 -2 4 6 1 -3

5. Function
A function is a relation where one value depends upon another value
Examples: y = 3x + 5
y = -8x + 12
y = x2
Functions have ONE rule:
Each x-value may only be used once
(one x-value cannot have multiple y-values)

6. Bellwork 2 4 6 1 3 1 3 9 Which of the following are functions? A B C DX Y 1 4 2 -1 9 -3 D E F 1 3 9 X Y 3 2 9 4 15 5 18

7. Vertical Line Test
If any vertical line goes through JUST ONE point, it IS a function
If any vertical line goes through MORE THAN ONE point, it is NOT a function

8. Function Notation
Instead of writing y = we often write f(x) = to show that we are working with a function of x
Examples: f(x) = 3x + 5
f(x) = -8x + 12
f(x) = x2
Examples: f(x) = 3x + 5
f(2) = 3(2) + 5 = = 11
f(-3) = 3(-3) + 5 = = -4

9. f(x) = -5x y = 2x + 1 f(x) = x2 y = x {(4, ),(-7, ),(8, ),(0, )} 7 -3
{(4, ),(-7, ),(8, ),(0, )}
f(x) = x2
y = x X Y 3 -2 6