Question

Please help quick will give brainliest!

Answer 1

Answer: Choice A) There must be a vertical asymptote at x = c

Explanation:

The first limit $\displaystyle \lim_{x\to c^{-}}h(x) = -\infty$ says that as x approaches c from the left side, the f(x) or y values approach negative infinity. So the graph goes down forever as x approaches this c value from the left side.

The limit $\displaystyle \lim_{x\to c^{+}}h(x) = \infty$ means that as x approaches c from the right side, the y values head off to positive infinity.

Either of these facts are enough to conclude that we have a vertical asymptote at x = c. We can think of it like an electric fence in which we can get closer to, but not actually touch it.