Question #N31
The function $f(x)$ is defined by $f(x) = \frac{1}{x-2} + 3$. What is the vertical asymptote of the graph of $y = f(x)$ in the xy-plane?
A. x = -2
B. x = 2
C. x = -3
D. x = 3
Correct Answer is: B
A vertical asymptote occurs where the denominator of a rational function equals zero. The denominator of $f(x)$ is $x-2$, which equals zero when $x = 2$. Therefore, the vertical asymptote of the graph of $y = f(x)$ is $x = 2$.