Worksheet: Graphing Functions with Negative Exponents

In this worksheet, we will practice graphing rational functions whose numerator is constant then we will analyze the function's domain, range, y-intercept, end behavior, continuity, and finally its decreasing and increasing intervals.

Q1:

Consider the function 𝑓 ( 𝑥 ) = 1 4 𝑥 .

State the domain and the range of the function.

  • ADomain: ( 0 , ) , range: ( 0 , )
  • BDomain: ( , 0 ) , range: ( 0 , )
  • CDomain: ( , 0 ) ( 0 , ) , range: ( , 0 )
  • DDomain: ( , 0 ) ( 0 , ) , range: ( 0 , )
  • EDomain: ( , ) , range: ( 0 , )

Find l i m 𝑓 ( 𝑥 ) .

  • A1
  • B
  • C
  • D0

Find l i m 𝑓 ( 𝑥 ) .

  • A0
  • B
  • C
  • D1

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

  • ANo
  • BYes, at 𝑥 = 0

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

  • AIncreasing over ( 1 , ) , decreasing over ( , 1 ) over
  • BIncreasing over ( , 1 ) , decreasing over ( 1 , )
  • CIncreasing over [ 0 , ) , decreasing over ( , 0 )
  • DIncreasing over ( , 0 ) , decreasing over ( 0 , )
  • EIncreasing over ( 0 , ) , decreasing over ( , 0 )

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