Question

The function g is graphed below, along with its asymptote.At what numbers in the interval (-4,4) is g discontinuous?If there is more than one number, separate them with commas.If there are no discontinuities, click on "None."

Answer 1

A function g(x) is discontinuous at x = p if the one-sided limits (from the left and from the right) are different.

For the given function g, we see that:

`\begin{gathered} \lim _(x\to-2^-)g(x)=-1 \\ \\ \lim _(x\to-2^(^+))g(x)=-3 \end{gathered}`

So, this function has a discontinuity at x = -2.

Now, for x = 1, we see that both side limits are infinity. So, they are the same. Thus, this function does not have a discontinuity at this point.

Therefore, the answer is -2