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{ = }(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)(x^2+9x+8)/(3x^2-24x-27)\text{ = }(-7)/(30)`
`\lim _(x\to9)(x^2+9x+8)/(3x^2-24x-27)\text{ =Doesn't exists.}`

So, x = 9 corresponds to a ertical asymptote