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Lesson: Determining Horizontal and Vertical Asymptotes

In this lesson, we discuss the definition of asymptotes, then focus on the horizontal and vertical asymptotes of a function and learn how to evaluate them.

Worksheet: Determining Horizontal and Vertical Asymptotes • 9 Questions

Q1:

Find the vertical and horizontal asymptotes of the function .

AThe function has no vertical asymptote and a horizontal asymptote at .
BThe function has a vertical asymptote at and no horizontal asymptote.
CThe function has no vertical asymptote and a horizontal asymptote at .
DThe function has no vertical asymptote and a horizontal asymptote at .
EThe function has a vertical asymptote at and no horizontal asymptote.

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 ?

Q4:

What are the two asymptotes of the hyperbola ?

Q5:

The graph of equation is a hyperbola only if . In that case, what are the two asymptotes?

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