Question
Determine the vertical asymptotes of the graph of the function. Give your answers as equations in exact form \[ g(x)=\frac{5}{x-3} \] Separate multiple equations with commas as necessary. Select "None" if applicable. Equation(s) of the vertical asymptote(s):
Ask by Lindsey Carlson. in the United States
Mar 17,2025
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Tutor-Verified Answer
Answer
**Equation of the vertical asymptote:** \( x = 3 \)
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The Deep Dive
To determine the vertical asymptotes of the function \( g(x) = \frac{5}{x-3} \), we look for values of \( x \) that make the denominator zero since vertical asymptotes occur where the function approaches infinity. Setting the denominator equal to zero, we have: \[ x - 3 = 0 \] Solving this gives \( x = 3 \). Therefore, the equation of the vertical asymptote is: \[ x = 3 \] Equation(s) of the vertical asymptote(s): \( x = 3 \)