# Worksheet: Monomial Functions

In this worksheet, we will practice graphing and analyzing monomial functions.

Q1:

Consider the function .

Which of the following shows the graph of ?

• A • B • C • D What is the -intercept of the function?

What is the domain of ?

• A
• B
• C

What is the range of ?

• A
• B
• C

On what interval is the function increasing?

• A
• B
• C

On what interval is the function decreasing?

• A
• B
• C

What happens to the value of as ?

• A
• B

What happens to the value of as ?

• A
• B

Q2:

Consider the function .

Which of the following shows the graph of ?

• A • B • C • D What is the -intercept of the function?

What is the domain of ?

• A
• B
• C

What is the range of ?

• A
• B
• C

On what interval is the function increasing?

• AThere are no intervals on which the function is increasing.
• B
• C

On what interval is the function decreasing?

• AThere are no intervals on which the function is decreasing.
• B
• C

What happens to the value of as ?

• A
• B

What happens to the value of as ?

• A
• B

Q3:

The figure shows the graph of . Consider the behavior of the function .

State the domain and the range of .

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Find .

Find .

State where the function has a discontinuity.

• A
• B
• C
• D

State the intervals over which is increasing and decreasing.

• AIncreasing over , decreasing over
• BIncreasing over , decreasing over
• CIncreasing over , decreasing over
• DIncreasing over , decreasing over
• EIncreasing over , decreasing over

Q4:

Consider the function .

State the domain and range of the function.

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Evaluate .

• A0
• B
• C

State the interval over which the function is continuous.

• A
• B
• C
• D
• E

State the intervals over which the function is increasing and/or decreasing.

• AIncreasing on
• BIncreasing on
• CIncreasing on , decreasing on
• DIncreasing on
• EDecreasing on

Q5:

Consider the function .

State the domain and range of the function.

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Find .

• A
• B
• C0

Find .

• A
• B0
• C

State the intervals over which the function is continuous.

• A
• B
• C
• D
• E

State the intervals over which the function is increasing and decreasing.

• ADecreasing on , increasing on
• BDecreasing on , increasing on
• CDecreasing on , increasing on
• DDecreasing on , increasing on

Q6:

Consider the function .

State the domain and range of the function.

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Evaluate .

State the interval over which the function is continuous.

• A
• B
• C
• D
• E

State the intervals over which the function is increasing and/or decreasing.

• AIncreasing on
• BIncreasing on , decreasing on
• CDecreasing on
• DDecreasing on , increasing on
• EDecreasing on

Q7:

Consider the function .

State the domain and range of the function.

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Find .

Find .

State where the function has a discontinuity.

• A
• B
• C

State the intervals over which the function is increasing and decreasing.

• AIncreasing over , decreasing over
• BIncreasing over , decreasing over
• CIncreasing over , decreasing over
• DIncreasing over and , never decreasing
• EIncreasing over , decreasing over

Q8:

Consider the function .

State the domain and the range of the function.

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Find .

• A0
• B
• C1
• D

Find .

• A
• B1
• C
• D0

Is the function undefined at any values? If yes, state the values.

• ANo
• BYes, at

State the intervals over which the function is increasing and decreasing.

• AIncreasing over , decreasing over
• BIncreasing over , decreasing over
• CIncreasing over , decreasing over
• DIncreasing over , decreasing over over
• EIncreasing over , decreasing over