which function has a vertical asymptote at x = 2? select one: a. f(x)=x/(x - 2) b. f(x)=(x + 2)/x c. f(x)=(x…

Explanation:

Step1: Recall vertical - asymptote rule

A rational function $y = \frac{f(x)}{g(x)}$ has a vertical asymptote at $x = a$ when $g(a)=0$ and $f(a)\neq0$.

Step2: Check option a

For $f(x)=\frac{x}{x - 2}$, when $x = 2$, $g(2)=2 - 2=0$ and $f(2)=2\neq0$. So it has a vertical asymptote at $x = 2$.

Step3: Check option b

For $f(x)=\frac{x + 2}{x}$, when $x = 2$, $g(2)=2\neq0$. So it has no vertical asymptote at $x = 2$.

Step4: Check option c

For $f(x)=\frac{x - 2}{x}$, when $x = 2$, $g(2)=2\neq0$. So it has no vertical asymptote at $x = 2$.

Step5: Check option d

For $f(x)=\frac{x}{x + 2}$, when $x = 2$, $g(2)=2+2 = 4\neq0$. So it has no vertical asymptote at $x = 2$.

Answer:

A. $f(x)=\frac{x}{x - 2}$