# Worksheet: Graphing Functions with Rational Exponents

In this worksheet, we will practice graphing functions with rational exponents then analyzing the function's domain, range, y-intercept, end behavior, continuity, and finally its decreasing and increasing intervals.

**Q1: **

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

**Q2: **

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 .

- A0
- B
- 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

**Q3: **

Consider the function .

State the domain and range of the function.

- ADomain: , range:
- BDomain: , range:
- CDomain: , range:
- DDomain: , range:
- EDomain: , range:

Evaluate .

- A
- B0
- 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 , decreasing on
- CIncreasing on
- DIncreasing on
- EDecreasing on

**Q4: **

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.

- ADecreasing on
- BIncreasing on
- CIncreasing on , decreasing on
- DDecreasing on
- EDecreasing on , increasing on

**Q5: **

Consider the function .

State the domain and range of the function.

- ADomain: , range:
- BDomain: , range:
- CDomain: , range:
- DDomain: , range:
- EDomain: , range:

Find .

Find .

- A
- B
- C0

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 , decreasing over
- EIncreasing over and , never decreasing