Question

find equations for the vertical asymptotes, if any, for the following rational function.
$f(x) = \frac{5}{x - 1}$
answer
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none

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).

Step2: Find denominator zero

For \( f(x)=\frac{5}{x - 1} \), denominator is \( x - 1 \). Set \( x - 1=0 \).
Solve: \( x=1 \). Check numerator: \( 5
eq0 \) at \( x = 1 \), so vertical asymptote at \( x = 1 \).

Answer:

\( x = 1 \)