# 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

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