World 2-1Functions, Relations, Domain and Range

Recall that a FUNCTION takes 1 input and produces only 1 outputfor that exact input.

Mr. Function

A RELATION, takes 1 input, butmay produce multiple outputs forthat given input.

Ms. Relation

Function Notation

f(x) = 4x +10

output input

(x, f(x) )

(1) Graph - Vertical Line Test

Function ____ Function _____

A vertical line touches the curve at ONLY 1 spot at a time

YES NO

A vertical line touches MORE THAN 1 spot at a time.

Function

Relation

(2) Table of Values

Each x value has only ONE y value.

An x value has MORE THAN ONE y value

x y

0 2

1 4

3 6

5 8

x y

1 0

2 1

4 3

4 5

Function ____YES Function ____NO

Function

Relation

(3) Mapping Diagram

YES NOFunction ____

A Bf

2

3

5

7

4

6

10

14

Source Target

Each source value has only ONE target value

Function ____

A Br

2

3

5

7

4

6

10

11

A source value has MORE THAN ONE target value

FunctionRelation

Ex. 1 Calculate the output value of each function

Not every x value can be inputted into a function. For example,

Orange YES Brick NO

x yx y

-4 0

0 2

5 3

x y

you cannot input a value that will force the function to take a square root of a negative or divide by zero.

Asymptote

x y

1 6

2 3

3 2

6 1

-1 -6

-2 -3

-3 -2

-6 -1

DOMAIN: The set of all possible x values that can be inputted into a function

RANGE: The set of all possible y values that are outputted from a function.

x greater than 5

x less than or equal to 10

y is between 0 and 100

z is at most 50

INTERVAL NOTATION SET BUILDER NOTATION

x is 5, 6 or 7

(4,4)

(-5,-2)

Ex. 2 Determine the domain and range

(0,0)

D: _________

R: _________

D: _________

R: _________

Domain and Range Challenge

1. Find the Domain and Range

D: ___________ R: ___________[-6,5] [1,6]

2. Find the Domain and Range

Domain: ___________ Range: ___________[-8,6[ ]-4,5]

3. Find the Domain and Range

Domain: ___________ Range: __________]-∞, ∞[ [-1, ∞[

4. Find the Domain and Range

D: ___________ R: ___________[-1, ∞[ ] -∞, ∞[

5. Find the Domain and Range

D: ___________ R: ___________]-6, 6[ ] -5, 5[

6. Find the Domain and Range

D: _______________ R: ___________[-∞, 0[ U ]0, ∞[ ] 0, ∞[

7. Find the Domain and Range

D: ___________ R: ___________{1,3,5} {4,5,6}

Homework

World 2-1 Homework