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Lesson: Graphing Functions with Rational Exponents

Worksheet • 5 Questions

Q1:

The figure shows the graph of 𝑓 ( π‘₯ ) = π‘₯    .

Consider the behavior of the function 𝑔 ( π‘₯ ) = ( π‘₯ + 2 ) + 5    .

State the domain and the range of 𝑔 .

  • ADomain: ( βˆ’ ∞ , βˆ’ 2 ) βˆͺ ( βˆ’ 2 , ∞ ) , range: ( 5 , ∞ )
  • BDomain: ( βˆ’ ∞ , 5 ) βˆͺ ( 5 , ∞ ) , range: ( βˆ’ 2 , ∞ )
  • CDomain: ( βˆ’ ∞ , 2 ) βˆͺ ( 2 , ∞ ) , range: ( 5 , ∞ )
  • DDomain: ( βˆ’ ∞ , 5 ) βˆͺ ( 5 , ∞ ) , range: ( 2 , ∞ )
  • EDomain: ( βˆ’ ∞ , βˆ’ 2 ) βˆͺ ( βˆ’ 2 , ∞ ) , range: ( βˆ’ 5 , ∞ )

Find l i m  β†’  ∞ 𝑔 ( π‘₯ ) .

Find l i m  β†’ ∞ 𝑔 ( π‘₯ ) .

State where the function has a discontinuity.

  • A π‘₯ = βˆ’ 2
  • B π‘₯ = 2
  • C π‘₯ = 5
  • D π‘₯ = βˆ’ 5

State the intervals over which 𝑔 is increasing and decreasing.

  • AIncreasing over ( βˆ’ ∞ , βˆ’ 2 ) , decreasing over ( βˆ’ 2 , ∞ )
  • BIncreasing over ( βˆ’ 2 , ∞ ) , decreasing over ( βˆ’ ∞ , βˆ’ 2 )
  • CIncreasing over ( βˆ’ ∞ , 5 ) , decreasing over ( 5 , ∞ )
  • DIncreasing over ( βˆ’ ∞ , βˆ’ 5 ) , decreasing over ( 5 , ∞ )
  • EIncreasing over ( βˆ’ ∞ , 2 ) , decreasing over ( 2 , ∞ )

Q2:

Consider the function .

State the domain and range of the function.

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

Evaluate .

  • A
  • B
  • C0

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

Q3:

Consider the function 𝑓 ( π‘₯ ) = 4 π‘₯   .

State the domain and range of the function.

  • ADomain: ( βˆ’ ∞ , ∞ ) , range: [ 0 , ∞ )
  • BDomain: ( βˆ’ ∞ , ∞ ) , range: ( βˆ’ ∞ , ∞ )
  • CDomain: ( βˆ’ ∞ , ∞ ) , range: ( 0 , ∞ )
  • DDomain: ( βˆ’ ∞ , 0 ) , range: ( 0 , ∞ )
  • EDomain: ( βˆ’ ∞ , 0 ) , range: [ 0 , ∞ )

Find l i m  β†’  ∞ 𝑓 ( π‘₯ ) .

  • A0
  • B ∞
  • C βˆ’ ∞

Find l i m  β†’ ∞ 𝑓 ( π‘₯ ) .

  • A0
  • B ∞
  • C βˆ’ ∞

State the intervals over which the function is continuous.

  • A ( βˆ’ ∞ , ∞ )
  • B ( βˆ’ ∞ , 0 ]
  • C ( βˆ’ ∞ , 0 )
  • D [ 0 , ∞ )
  • E ( 0 , ∞ )

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

  • ADecreasing on ( βˆ’ ∞ , 0 ) , increasing on ( 0 , ∞ )
  • BDecreasing on ( 0 , ∞ ) , increasing on ( βˆ’ ∞ , 0 )
  • CDecreasing on [ 0 , ∞ ) , increasing on ( βˆ’ ∞ , 0 ]
  • DDecreasing on ( βˆ’ ∞ , 0 ] , increasing on [ 0 , ∞ )

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
  • CDecreasing on
  • DIncreasing on , decreasing 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
  • B0
  • C

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