find all vertical asymptotes of the following function.\n\nf(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): [ \begin{align*} 2x+18&=0\ 2x&=- 18\ x&=-9 \end{align*} ]

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

Substitute (x = - 9) into the numerator (x - 2): (-9-2=-11\neq0)

Answer:

The vertical asymptote is (x=-9)