Question

Which statement describes why x = -2 is an asymptote for the graphed function?

Answer 1

The answer is B: the function approaches positive infinity as x approaches -2.

In fact, when you read a limit like

$\displaystyle\lim_{x \to c} f(x) = k$

You mean that, if you approeach the point c on the x axis, the function approaches the value k on the y axis.

In this case, k in positive infinity, so we're saying that, when you approach -2 along the x axis, the function "explodes" to positive infinity, which means that x = -2 is a vertical asymptote for the function.