Question

Find the equation of the oblique asymptote for the following rational function. Give an equation of the backbone of the function if one exists…

Answer 1

We want to find the oblique asymptote for the following function

`f(x)=(x^3-7x-6)/(x^2-2x-15)`

To find the oblique asymptote, we just need to effectuate the division and analyse its behavior as it goes to infinity.

Doing the division, we have

`(x^3-7x-6)/(x^2-2x-15)=x+2+(12x+24)/(x^2-2x-15)`

The rational term approaches 0 as the variable approaches infinity.

Thus, the oblique asymptote is y = x + 2