In this lesson, we will learn how to find the equations of the oblique asymptotes of functions, especially rational functions.
Students will be able to
Q1:
The figure shows the graph of π(π₯)=6π₯β3π₯+10π₯β2π₯+13π₯+4π₯β1οͺο©ο¨ο© and an oblique asymptote π¦=ππ₯+π.
By synthetic division, determine the value of π.
By considering the behavior of π(π₯)β2π₯ as π₯ goes to Β±β, determine the value of π.
Q2:
The figure shows the graph of π(π₯)=2β6π₯+4π₯+6π₯β5π₯π₯βπ₯βπ₯+1ο¨ο©οͺο©ο¨ together with its asymptotes π₯=1 and π₯=β1 and an oblique line πΏ.
Determine the equation of πΏ giving your answer in the form π¦=ππ₯+π.
Q3:
The figure shows the graph of the function π(π₯)=π(π₯)(π₯β1)(π₯+2) with vertical asymptotes at π₯=1 and π₯=β2 and oblique asymptote π¦=4π₯β4.
Determine the polynomial π given the points shown on the graph.
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