Question

question
find all vertical asymptotes of the following function.
f(x)=\frac{3 x^{2}+9 x - 162}{3 x - 7}
answer attempt 2 out of 2
one vertical asymptote

Explanation:

Step1: Find the zero of the denominator

Set the denominator \(3x - 7=0\).
Solving for \(x\), we get \(x=\frac{7}{3}\).

Step2: Check if the numerator is non - zero at this \(x\) value

Substitute \(x = \frac{7}{3}\) into the numerator \(3x^{2}+9x - 162\).

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Answer:

The vertical asymptote is \(x = \frac{7}{3}\)