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Worksheet: Identifying and Using the Asymptotes of Rational Functions

Q1:

Determine the vertical and horizontal asymptotes of the function .

  • AThe vertical asymptote is at , and the function has no horizontal asymptote.
  • BThe function has no vertical asymptote, and the horizontal asymptote is at .
  • CThe vertical asymptote is at , and the horizontal asymptote is at .
  • DThe vertical asymptote is at , and the horizontal asymptote is at .
  • EThe vertical asymptote is at , and the horizontal asymptote is at .

Q2:

Determine the vertical and horizontal asymptotes of the function .

  • AThe vertical asymptote is at , and the function has no horizontal asymptote.
  • BThe function has no vertical asymptote, and the horizontal asymptote is at .
  • CThe vertical asymptote is at , and the horizontal asymptote is at .
  • DThe vertical asymptote is at , and the horizontal asymptote is at .
  • EThe vertical asymptote is at , and the horizontal asymptote is at .

Q3:

What are the two asymptotes of the hyperbola ?

  • A
  • B
  • C
  • D
  • E

Q4:

Find the domain and range of the function .

  • AThe domain is and the range is .
  • BThe domain is and the range is .
  • CThe domain is and the range is .
  • DThe domain is and the range is .

Q5:

Determine the domain and the range of the function in .

  • AThe domain is , and the range is .
  • BThe domain is , and the range is .
  • CThe domain is , and the range is .
  • DThe domain is , and the range is .

Q6:

Which of the following graphs represents ?

  • A(d)
  • B(c)
  • C(a)
  • D(b)

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