Question

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}\\)?

• the graph has no vertical asymptotes.
• the graph has one vertical asymptote.
• the graph has two vertical asymptotes.
• the number of asymptotes depends on whether the rational expression is simplified.

Explanation:

Factor the numerator and denominator of the function

$$ f(x) = \frac{2x - 4}{x^2 - 4} = \frac{2(x - 2)}{(x - 2)(x + 2)} $$

Simplify the expression and identify restrictions

$$
LATEXBLOCK0
$$

Determine the vertical asymptotes

$$
LATEXBLOCK1
$$

Answer:

• The graph has no vertical asymptotes.
• The graph has one vertical asymptote. (Correct answer)
• The graph has two vertical asymptotes.
• The number of asymptotes depends on whether the rational expression is simplified.