# 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 .

Determine the equation of giving your answer in the form .

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**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.

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**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 .

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

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- B, , ,
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- D, , and and can take any values.
- E, , ,

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

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- B, , ,
- C, , ,
- D, , ,
- E, , ,

**Q5: **

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

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**Q6: **

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

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**Q7: **

Determine the oblique asymptote to the curve .

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**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 .

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