Functions and Relations Not relationships Relations.

Functions and Relations

Not relationships

Relations

Functions and Relations

Standard: 18.0 Students determine whether a relation defined by a

graph, a set of ordered pairs, or a symbolic expression is a function

and justify the conclusion.

Objective:

•The students should be able to determine if a set of ordered pairs is a function.

•Apply the vertical line test to determine if a graph is a function

Vocabulary

Relation

Function

Input

Output

Graph

Domain

Domain RangeVertical line testDiscrete Continuous

Why do we need functions?

What are functions? For every input, the function returns exactly one output.

What are functions?

Even though two different inputs may give the same outputFor example: f(x) = x2

(3,9) and (-3, 9)f(x) is still a function. Every x has a unique y, not every y has a unique x.

Birthday Relations

What are functions? Determine if the set of ordered pairs is a

function? Explain(5,2) (4,1) (3,0) (2,-1) (1,-2) (0,-3)

(2,2) (3,3) (4,4) (5,5) (6,6)

(2,1) (2,2) (2,3) (2,4) (2,5)

(-2,2) (-4,2) (-6,2) (-8,2)

(9,-9) (8,-8) (7,-7) (9,-6)

No

No

Yes

Yes

No

No

Yes

YesNo

Yes

What are functions?

A vertical line should intersect the graph at exactly one point.

Vertical Line Test

Use the Vertical Line Test to determine if the

graph represents a function.

Use the Vertical Line Test to determine if the

graph represents a function.

Use the Vertical Line Test to determine if the

graph represents a function.

Congratulations

You Are Correct!!!!!!

SorryTry again