Question

find equations for the vertical asymptotes, if any, for the following rational function.
$f(x) = \frac{7}{x - 8}$
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3 points
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Explanation:

Step1: Recall vertical asymptote rule

For a rational function \( f(x)=\frac{N(x)}{D(x)} \), vertical asymptotes occur where \( D(x) = 0 \) (and \( N(x)
eq0 \) at those points).
Here, \( N(x)=7 \) (non - zero constant) and \( D(x)=x - 8 \).

Step2: Solve \( D(x)=0 \)

Set \( x - 8=0 \).
Solving for \( x \), we add 8 to both sides of the equation: \( x=8 \).
Since \( N(8) = 7
eq0 \), \( x = 8 \) is a vertical asymptote.

Answer:

\( x = 8 \)