Question

find all vertical asymptotes of the following function.

f(x) = \frac{x - 2}{2x + 18}

Explanation:

Step1: Find the denominator

The denominator of the function \(f(x)=\frac{x - 2}{2x+18}\) is \(2x + 18\).

Step2: Set the denominator equal to zero

Set \(2x+18 = 0\).
Solve for \(x\):

$$
LATEXBLOCK0
$$

Step3: Check if the numerator is non - zero at \(x=-9\)

Substitute \(x = - 9\) into the numerator \(x - 2\): \(-9-2=-11
eq0\)

Answer:

The vertical asymptote is \(x=-9\)