Question

Determine the holes, vertical asymptotes and horizontal asymptotes of the rational function y=(3x^2+10x-8)/(x^2+7x+12)

Answer 1

First, we have to factor both the numerator and the denominator$y= \frac{(3x-2)(x+4)}{(x+3)(x+4)}$

A hole in a rational function is defined as any input that leads to the numerator and denominator to equal zero as such, x=-4

The vertical asymptote can be found at x=-4 and x=-3

The horizontal asymptote since the numerator has the same degree as the denominator there is a horizontal asymptote. which is at y= 3