# 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 .

- ADomain: , range:
- 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.

- ADomain: , range:
- 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.

- ADomain: , range:
- 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.

- ADomain: , range:
- 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.

- ADomain: , range:
- 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.

- ADomain: , range:
- 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