In this lesson, we will learn how to find the equations of the oblique asymptotes of functions, especially rational functions.
Q1:
The figure shows the graph of 𝑓(𝑥)=6𝑥−3𝑥+10𝑥−2𝑥+13𝑥+4𝑥−1 and an oblique asymptote 𝑦=𝑚𝑥+𝑐.
By synthetic division, determine the value of 𝑚.
By considering the behavior of 𝑓(𝑥)−2𝑥 as 𝑥 goes to ±∞, determine the value of 𝑐.
Q2:
The figure shows the graph of 𝑓(𝑥)=2−6𝑥+4𝑥+6𝑥−5𝑥𝑥−𝑥−𝑥+1 together with its asymptotes 𝑥=1 and 𝑥=−1 and an oblique line 𝐿.
Determine the equation of 𝐿 giving your answer in the form 𝑦=𝑚𝑥+𝑐.
Q3:
The figure shows the graph of the function 𝑓(𝑥)=𝑃(𝑥)(𝑥−1)(𝑥+2) with vertical asymptotes at 𝑥=1 and 𝑥=−2 and oblique asymptote 𝑦=4𝑥−4.
Determine the polynomial 𝑃 given the points shown on the graph.
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