Thread: Graphing the reciprocal of a cubic function

Hi there,

Currently I am taking an independant learning class to earn my grade 12 Advanced Functions credit. Recently I've been learning about sketching reciprocal functions and determining where horizontal and vertical asymptotes will occur. I am very stuck on one question in particular:

Determine the vertical asymptotes of g(x) = x + 2 / x^3 - x^2 - x + 1 and sketch the graph near the asymptotes.

I'm not even sure how to start here, normally I would find the asymptotes by setting the denominator equal to zero, however I do no know how to solve 0 = x^3 - x^2 - x + 1

Any help here would be much appreciated, thanks in advance!

Originally Posted by Lethargic

Hi there,

Currently I am taking an independant learning class to earn my grade 12 Advanced Functions credit. Recently I've been learning about sketching reciprocal functions and determining where horizontal and vertical asymptotes will occur. I am very stuck on one question in particular:

Determine the vertical asymptotes of g(x) = x + 2 / x^3 - x^2 - x + 1 and sketch the graph near the asymptotes.

I'm not even sure how to start here, normally I would find the asymptotes by setting the denominator equal to zero, however I do no know how to solve 0 = x^3 - x^2 - x + 1

Any help here would be much appreciated, thanks in advance!

Let p(x) = x^3 - x^2 - x + 1. By inspection, p(1) = 0 therefore x - 1 is a factor of x^3 - x^2 - x + 1. Divide x^3 - x^2 - x + 1 by x - 1 using polynomial long division to get the other quadratic factor. Find the zeros of the quadratic factor in the usual way.

Thanks!

I actually just learned polynomial long division 2 lessons ago, I can't believe I didn't think of that