Lesson: Oblique Asymptotes

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

Worksheet: 7 Questions

Q1:

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

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

Q2:

The figure shows the graph of 𝑓(π‘₯)=2βˆ’6π‘₯+4π‘₯+6π‘₯βˆ’5π‘₯π‘₯βˆ’π‘₯βˆ’π‘₯+1οŠͺ 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‘šπ‘₯+𝑐.

Q3:

The figure shows the graph of the function 𝑓(π‘₯)=𝑃(π‘₯)(π‘₯βˆ’1)(π‘₯+2) with vertical asymptotes at π‘₯=1 and π‘₯=βˆ’2 and oblique asymptote 𝑦=4π‘₯βˆ’4.

Determine the polynomial 𝑃 given the points shown on the graph.
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