Question

Find all vertical asymptotes of the following function.f(x) ==x² + 9x + 83x2 – 24x – 27SUBJECT: ALG2 need help being able to find if it’s a NON VERTICAL asymptote, ONE or TWO vertical asymptotes.

Answer 1

Given:

$f(x)\text{ = }\frac{x^2+9x+8}{3x^2-24x-27}$

First, we determine the excluded values:

3x² - 24x - 27 = 0

3(x² - 8x - 9) = 0

3(x - 9)(x + 1) = 0

x ≠ -1 and x ≠ 9

Now we evaluate limits on -1 and 9:

$\lim _{x\to-1}\frac{x^2+9x+8}{3x^2-24x-27}\text{ = }\frac{-7}{30}$$\lim _{x\to9}\frac{x^2+9x+8}{3x^2-24x-27}\text{ =Doesn't exists.}$

So, x = 9 corresponds to a ertical asymptote