1.9.3 quiz: finding vertical asymptotes which of the following rational functions is graphed below? a. f(x)…

1.9.3 quiz: finding vertical asymptotes which of the following rational functions is graphed below? a. f(x) = 1/(x + 2) b. f(x) = 2/x c. f(x) = 1/(2x) d. f(x) = 1/(x - 2)

1.9.3 quiz: finding vertical asymptotes which of the following rational functions is graphed below? a. f(x) = 1/(x + 2) b. f(x) = 2/x c. f(x) = 1/(2x) d. f(x) = 1/(x - 2)

Answer

Explanation:

Step1: Recall vertical - asymptote rule

The vertical asymptote of a rational function $F(x)=\frac{a}{x - h}$ is at $x = h$.

Step2: Identify the vertical asymptote from the graph

The vertical asymptote of the given graph is at $x = 2$.

Step3: Match the function with the asymptote

For the function $F(x)=\frac{1}{x - 2}$, when $x-2=0$ (i.e., $x = 2$), the function is undefined. So the vertical asymptote is $x = 2$.

Answer:

D. $F(x)=\frac{1}{x - 2}$