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Lesson: Identifying and Using the Asymptotes of Rational Functions

Sample Question Videos

Worksheet • 7 Questions • 2 Videos

Q1:

Find the domain of the function 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 3 6 π‘₯ π‘₯ + 6 π‘₯ 3 2 .

  • A ℝ βˆ’ { βˆ’ 6 , 0 }
  • B ℝ βˆ’ { βˆ’ 1 2 , βˆ’ 6 }
  • C { βˆ’ 6 , 0 }
  • D ℝ βˆ’ [ βˆ’ 6 , 0 ]

Q2:

Determine the vertical and horizontal asymptotes of the function 𝑓 ( π‘₯ ) = βˆ’ 1 + 3 π‘₯ βˆ’ 4 π‘₯ 2 .

  • A The vertical asymptote is at π‘₯ = 0 , and the horizontal asymptote is at 𝑦 = βˆ’ 1 .
  • B The vertical asymptote is at π‘₯ = βˆ’ 1 , and the function has no horizontal asymptote.
  • C The vertical asymptote is at 𝑦 = βˆ’ 1 , and the horizontal asymptote is at π‘₯ = 0 .
  • D The function has no vertical asymptote, and the horizontal asymptote is at 𝑦 = 0 .
  • E The vertical asymptote is at π‘₯ = 3 , and the horizontal asymptote is at 𝑦 = βˆ’ 4 .

Q3:

Determine the vertical and horizontal asymptotes of the function 𝑓 ( π‘₯ ) = 4 + 2 π‘₯ βˆ’ 3 π‘₯ 2 .

  • A The vertical asymptote is at π‘₯ = 0 , and the horizontal asymptote is at 𝑦 = 4 .
  • B The vertical asymptote is at π‘₯ = 4 , and the function has no horizontal asymptote.
  • C The vertical asymptote is at 𝑦 = 4 , and the horizontal asymptote is at π‘₯ = 0 .
  • D The function has no vertical asymptote, and the horizontal asymptote is at 𝑦 = 0 .
  • E The vertical asymptote is at π‘₯ = 2 , and the horizontal asymptote is at 𝑦 = βˆ’ 3 .
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