Question

find all vertical asymptotes of the following function.

$$ f ( x ) = \frac { 3 x + 30 } { x - 6 } $$

Explanation:

Step1: Recall the definition of vertical asymptote

A vertical asymptote occurs at \(x = a\) if the denominator of a rational function is zero at \(x=a\) and the numerator is non - zero at \(x = a\).
For the function \(f(x)=\frac{3x + 30}{x-6}\), set the denominator equal to zero: \(x-6=0\).

Step2: Solve for \(x\)

Solving the equation \(x - 6=0\) gives \(x=6\).
Now, check the value of the numerator at \(x = 6\). Substitute \(x = 6\) into the numerator \(3x+30\): \(3\times6+30=18 + 30=48
eq0\).

Answer:

\(x = 6\)