Worksheet: Graphing Rational Functions with Transformations

In this worksheet, we will practice graphing reciprocal functions and their vertical and translating the graphs of vertical and horizontal asymptotes.

Q1:

The graph shows 𝑦 = 𝑘 ( 𝑥 3 ) 2 . We can see that the intersection of its asymptotes is at ( 3 , 2 ) and that the points ( 0 . 5 , 1 . 5 ) and ( 1 . 5 , 1 ) are below and above the graph respectively. Determine the interval in which 𝑘 lies.

  • A 0 . 5 < 𝑘 < 3
  • B 2 < 𝑘 < 1
  • C 2 < 𝑘 < 0 . 5
  • D 1 . 5 < 𝑘 < 1 . 2 5
  • E 1 . 2 5 < 𝑘 < 1

Q2:

What function is represented in the figure below?

  • A 𝑓 ( 𝑥 ) = 1 𝑥 3
  • B 𝑓 ( 𝑥 ) = 1 𝑥 3
  • C 𝑓 ( 𝑥 ) = 1 𝑥 3
  • D 𝑓 ( 𝑥 ) = 1 𝑥 3

Q3:

Determine the domain and the range of the function 𝑓 ( 𝑥 ) = 1 𝑥 5 in .

  • A The domain is { 0 } , and the range is .
  • B The domain is , and the range is .
  • C The domain is , and the range is { 0 } .
  • D The domain is { 0 } , and the range is { 5 } .

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