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

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

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

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

Examples  

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

Function Notation Input Name of Function Output

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

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

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

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!

Vertical Line Test FUNCTION! NO! NO WAY! FUNCTION!

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

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

Given h(z) = z2 - 4z + 9, find h(-3) (-3)2-4(-3)+9 -3 30 9 + 12 + 9 h(-3) = 30

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

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