7.2 Functions and Graphs Objective: Understand functions. Fill out input-output tables. Determine if relations are functions.

What is a function? We will use a machine as an example of a function. Eli Whitney is famous for what invention? The Cotton Gin!!

input x domain Function (machine) output y range

Definition of Function A function is a relation in which each element of the domain is paired with exactly one element of the range.

4 ways to state relations Ordered Pairs Mapping Graphs Equations

Ordered Pairs (x, y) In order for a relation of ordered pairs to be a function the domain must not repeat. For example {(5,5), (5, 6)} is a relation, but is not a function. because when you have 5 as the input the output is 5 or 6 {(6,-3), (4,1), (7, -2), (-3, 1)} Function? {(1,2),(2, 3), (3, 4), (1, 3)} Function?

Mapping A relation in map form is a function if there is only one arrow coming from each element of the domain. Domain Range 1 2 4 6 2 4 6 8

Mapping Is this relation a function? Domain Range 1 2 3 4 9 8 7 6

Mapping Is this relation a function? Domain Range 1 2 3 4 5

Graphing Vertical Line Test (pencil test) If you graph the order pairs from the relation, if you can touch a vertical line to more than one point on the graph then it is not a function. Let’s go back and graph the ordered pairs and mapping examples and apply the vertical line test.

Input and Output Tables X Domain Output Y Range -3 -2 -1 1 2 3 2x+1

Input and Output Tables X Domain Output Y Range 4 2 5 3 -13 -3x + 2

The Vertical Line Test (aka The Pencil Test) If a vertical line that passes through the graph of the function touches the graph in more than one place then the graph is NOT a function. It is called the pencil test because most students use their pencil as a vertical line. Hint: Vertical is up and down.

Assignment 7.2 Worksheet