Lesson: Oblique Asymptotes

In this lesson, we will learn how to find the equations of the oblique asymptotes of functions, especially rational functions.

Worksheet: 2 Questions

Q1:

The figure shows the graph of 𝑓 ( π‘₯ ) = 6 π‘₯ βˆ’ 3 π‘₯ + 1 0 π‘₯ βˆ’ 2 π‘₯ + 1 3 π‘₯ + 4 π‘₯ βˆ’ 1 4 3 2 3 and an oblique asymptote 𝑦 = π‘š π‘₯ + 𝑐 .

By synthetic division, determine the value of π‘š .

By considering the behavior of 𝑓 ( π‘₯ ) βˆ’ 2 π‘₯ as π‘₯ goes to Β± ∞ , determine the value of 𝑐 .

Q2:

The figure shows the graph of 𝑓 ( π‘₯ ) = 2 βˆ’ 6 π‘₯ + 4 π‘₯ + 6 π‘₯ βˆ’ 5 π‘₯ π‘₯ βˆ’ π‘₯ βˆ’ π‘₯ + 1 2 3 4 3 2 together with its asymptotes π‘₯ = 1 and π‘₯ = βˆ’ 1 and an oblique line 𝐿 .

Determine the equation of 𝐿 giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .
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