Do Now: Make a K-W-L Chart Complete what you KNOW about functions

Functions October 17, 2017 Can I determine if a relationship is a function?

A function is a relation in which each input has exactly one output. Functions A function is a relation in which each input has exactly one output. f(x) y x

Function Notation Input Name of Function Output

Variables Variable x is called independent variable Variable y is called dependent variable We use f(x) instead of y.

What is the domain and range? The domain of a function is the set x. That is a collection of all possible inputs. The range of a function is the set of all possible outputs.

Function Rule An algebraic expression that defines a function For example: What is the function’s rule?

Five Representations of Functions Ordered Pairs Mapping Tables Graphs Equations

Tables – For each input, there is exactly one output

Turn and Talk Is this a function. WHY OR WHY NOT?

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

Mapping Functions

Are these functions YES NO

Carousel Start at any point in the carousel. Move clockwise around the room. Complete the following table: Is the relation a function? WHY or WHY NOT State the domain and range of each.