Question

find all vertical asymptotes of the following function.
$f(x) = \dfrac{3x^2 + 22x - 80}{2x + 8}$

Explanation:

Step1: Identify denominator zero

To find vertical asymptotes, set the denominator equal to zero: \(2x + 8 = 0\)

Step2: Solve for x

Subtract 8 from both sides: \(2x = -8\)
Divide by 2: \(x = -4\)

Step3: Check numerator at x=-4

Numerator: \(3(-4)^2 + 22(-4) - 80 = 3(16) - 88 - 80 = 48 - 88 - 80 = -120
eq 0\)
Since numerator ≠ 0 at x=-4, it's a vertical asymptote.

Answer:

The vertical asymptote is \(x = -4\)