Question

find all vertical asymptotes of the following function.

f(x)=\frac{3 x^{2}-108}{x - 9}

answer attempt 1 out of 2

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Explanation:

Step1: Factor the numerator

$$3x^{2}-108 = 3(x^{2}-36)=3(x + 6)(x - 6)$$

Step2: Analyze the function

The function \(f(x)=\frac{3(x + 6)(x - 6)}{x - 9}\). A vertical asymptote occurs at a value of \(x\) that makes the denominator equal to zero while the numerator is not zero at that value.
Set the denominator \(x-9=0\), we get \(x = 9\).
When \(x = 9\), the numerator \(3(9 + 6)(9 - 6)=3\times15\times3=135
eq0\)

Answer:

\(x = 9\)