# Worksheet: Oblique Asymptotes

In this worksheet, we will practice finding the equations of the oblique asymptotes of functions, especially rational functions.

Q1:

The figure shows the graph of and an oblique asymptote . By synthetic division, determine the value of .

By considering the behavior of as goes to , determine the value of .

Q2:

The figure shows the graph of together with its asymptotes and and an oblique line . • A
• B
• C
• D
• E

Q3:

The figure shows the graph of the function with vertical asymptotes at and and oblique asymptote . Determine the polynomial given the points shown on the graph.

• A
• B
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• D
• E

Q4:

We consider how the line of an oblique asymptote depends on the numerator of the rational function. Consider .

Simplify and then write the numerator of as a polynomial in descending powers of .

• A
• B
• C
• D

Using your answer above, find the conditions on , , , and under which the line is an oblique asymptote to the graph .

• A, , ,
• B, , ,
• C, , ,
• D, , and and can take any values.
• E, , ,

Find , , , and so that is an asymptote of , and that and .

• A, , ,
• B, , ,
• C, , ,
• D, , ,
• E, , ,

Q5:

The graph of is asymptotic to a line as . What is this line?

• A
• B
• C
• D
• E

Q6:

Use partial fractions to determine the line that is asymptotic to the curve .

• A
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• D
• E

Q7:

Determine the oblique asymptote to the curve .

• A
• B
• C
• D
• E

Q8:

Consider the function .

Find the equation of the oblique asymptote of the graph of to decide which of the following graphs is the graph of .

• A • B • C • D 