select the correct answer. which statement describes the vertical asymptote(s), if any, in the graph of the…

select the correct answer. which statement describes the vertical asymptote(s), if any, in the graph of the function (f(x)=\frac{2x - 4}{x^{2}-4})? a. the graph has no vertical asymptotes. b. the graph has one vertical asymptote. c. the graph has two vertical asymptotes. d. the number of asymptotes depends on whether the rational expression is simplified.

select the correct answer. which statement describes the vertical asymptote(s), if any, in the graph of the function (f(x)=\frac{2x - 4}{x^{2}-4})? a. the graph has no vertical asymptotes. b. the graph has one vertical asymptote. c. the graph has two vertical asymptotes. d. the number of asymptotes depends on whether the rational expression is simplified.

Answer

Explanation:

Step1: Find the values that make the denominator zero.

Set $x^{2}-4 = 0$. Using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$, where $a=x$ and $b = 2$, we have $(x + 2)(x - 2)=0$.

Step2: Solve for $x$.

If $(x + 2)(x - 2)=0$, then $x+2=0$ or $x - 2=0$. Solving $x+2=0$ gives $x=-2$, and solving $x - 2=0$ gives $x = 2$. These are the vertical asymptotes of the rational function $y=\frac{2x - 4}{x^{2}-4}$ (since the numerator $2x-4$ is not zero at $x=-2$ and $x = 2$).

Answer:

C. The graph has two vertical asymptotes.