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