Functions and Relations Pg. 57 – 58

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?

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

Function Notation Input Name of Function Output

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!

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

Class Example 2 FUNCTION! NO! NO WAY! FUNCTION!

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

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

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?

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)}

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

Student Example 3 Given h(x) = x2 – 4x + 9, find h(-3) (-3)2-4(-3)+9 30 -3 9 + 12 + 9 h(-3) = 30

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

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

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