What are the vertical asymptotes of the graph (y=\frac{1}{x^2-4})?

Correct answer: (x=-2) and (x=2)

A vertical asymptote occurs at an excluded input value where the function becomes unbounded. For \(y=\frac{1}{x^2-4}\), the denominator must not be zero. Solve \(x^2-4=0\), giving \(x^2=4\) and therefore \(x=2\) or \(x=-2\). Near either value, the denominator approaches zero while the numerator remains 1, so the function grows without bound. Thus option A is correct.

The equations of vertical asymptotes are written using \(x\), because they describe vertical lines. The lines are \(x=-2\) and \(x=2\). Values such as \(y=-2\) and \(y=2\) would describe horizontal lines, not vertical asymptotes. Both denominator zeros must be included.