Do NowDetermine if the correspondence would be a

function:Domain Correspondence Range

A family Each person’s weight

A set of positive numbers

Students at BMHS

Each person’s Geometry teacher A set of teachers

All of the states in the US

Each state’s members of the US

Senate

A set of US Senators

All NFL Quarterbacks

The team he plays for

A set of NFL Teams

All NFL Teams Their quarterbacks A set of quarterbacks

1)

Dom: [-4][-3] [0] [4] [5]Range: [-2] [-1] [0] [3]

[4]2)

Dom: [-5] [-3] [3] [5]Range: [0] [2] [3] [4] [5]

3) Function

Answers to Homework4) Not a function: -9 in the domain is

paired with 6 and 0.

5) Relation is a function. Each element in the domain is paired with one element in the range.

6) Relation is a function. 7) Relation is not a function, 4 in the

domain is paired with -1 and 9.8) Relation is not a function, 100 in

the domain is paired with 5 and -13.

9) Relation is a function. 10) Relation is not a function, -7 is

paired with 14 and 800.11) Relation is not a function. 5 is

paired with 7, -3, 4 and -1.12) Relation is a function.

Dom-35-470

Ran8-20-19

Dom-975-3

Ran6-208-5

HomeworkNeed help?

Look in section 2.1 – Relations & Functions in your textbook

Worksheet: Vertical Line Test & Function Notation

Unit 3: Domain & RangeDay 7: The Vertical Line Test

ObjectivesTo determine if a graph represents a functionTo use function notation to simplify functions

Relations & Functions ReviewWhat is domain?What is range? When is a relation a function?When is a relation NOT a function?

Relations & Functions on a GraphRelation is a Function Relation is NOT a function

x: domain

y: range

1,2 , 3,2 , 2, 4 , 0, 2 1,2 , 2,2 , 1, 4 , 4, 2

x: domain

y: range

The Vertical Line TestA graph represents a function if it is

impossible to draw a vertical line that intersects the graph more than once.

Function – passes VLT Not a Function – fails VLT

FunctionsDetermine if the following graph represents a

function.

Function – passes VLT Not a Function – fails VLT

FunctionsDetermine if the following graph represents a

function.

Not a Function – fails VLT Function – passes VLT

Function Notationx y

2 11

3 14

4 17

3 5y x

input

output

3 5f x x

input

input

Read f(x) as “f of x” IT IS NOT “f times x”

Function NotationA function f is given by

Find f(5).

Find f(d).

23 2 8f x x x

2_____ _____ ___ _3 2 _ 8f

25 53 852f

Whatever goes in the blank near the f, must go in every blank in the equation

85 75 10f

75 3f

24 43 842f

484 8 8f 644f

Find f(-4).

Find f(6x). 2

3 2 8d df d

23 2 8f d dd 26 863 26f x x x

23 36 2 6 86f xx x

2108 12 86f xx x

Did you meet today’s objective?How can you determine if a relation is a

function usinga graph?a set of points?a table?a mapping diagram?

How is function notation the same/different from a typical equation?