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Worksheet: Identifying and Using the Asymptotes of Rational Functions

Q1:

Determine the vertical and horizontal asymptotes of the function .

  • A The vertical asymptote is at , and the horizontal asymptote is at .
  • B The vertical asymptote is at , and the horizontal asymptote is at .
  • C The function has no vertical asymptote, and the horizontal asymptote is at .
  • D The vertical asymptote is at , and the horizontal asymptote is at .
  • E The vertical asymptote is at , and the function has no horizontal asymptote.

Q2:

Determine the vertical and horizontal asymptotes of the function .

  • A The vertical asymptote is at , and the horizontal asymptote is at .
  • B The vertical asymptote is at , and the horizontal asymptote is at .
  • C The function has no vertical asymptote, and the horizontal asymptote is at .
  • D The vertical asymptote is at , and the horizontal asymptote is at .
  • E The vertical asymptote is at , and the function has no horizontal asymptote.

Q3:

What are the two asymptotes of the hyperbola ?

  • A
  • B
  • C
  • D
  • E

Q4:

Find the domain and range of the function .

  • A The domain is and the range is .
  • B The domain is and the range is .
  • C The domain is and the range is .
  • D The domain is and the range is .

Q5:

Determine the domain and the range of the function in .

  • A The domain is , and the range is .
  • B The domain is , and the range is .
  • C The domain is , and the range is .
  • D The domain is , and the range is .

Q6:

Which of the following graphs represents ?

  • A(a)
  • B(b)
  • C(d)
  • D(c)

Q7:

What function is represented in the figure below?

  • A
  • B
  • C
  • D

Q8:

What function is represented in the figure below?

  • A
  • B
  • C
  • D