Introduction to Functions

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

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

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

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)

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

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

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 = 6 + 5 = 11 f(-3) = 3(-3) + 5 = -9 +5 = -4

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