3.2 Representing Functions Objectives The student will be able to: 1. To determine if a relation is a function. To find the value of a function. Indicators: PFA #1, PFA#3, PFA#4, PFA#7, PFA#8, PFA#9 Designed by Skip Tyler, Varina High School Modified by Anny Lin, Crestwood Middle School

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

Function notation For equations that are function can be written in a form called function notation. Consider 3x+y=1 Equation y=1-3x Function notation f(x)=1-3x

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

Determine whether each relation is a function. Explain. This mapping represents a relation that is not a function. The element –3 in the domain is paired with both 1 and 4 in the range. If you are given that x = -3, you cannot determine the value of y.

The table represents a function since, for each element of the domain, there is only one corresponding element in the range. It does not matter if two elements of the domain are paired with the same element in the range.

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

Is there any way to tell if it is a function by just looking at the graph? Yes, there is.

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

Determine whether 3x+y=1 represents a function. Make a table and plot points to graph the equation. X Y 1 -2 2 3

X Y 1 -2 2 -5 3 -8

Yes, it is.

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

Homework: Page 152 15-20 all, 27-32 all, 39-48 all