Which of the following is guaranteed by the Intermediate Value Theorem, if f is a continuous function on the closed interval [−13, −5] where f(−13) = 4 and f(−5) = 11?

Answer 1

I think your question is incomplete, but essentially the IVT implies that your function f will output any and all values between 4 and 11 on its interval.

If f is continuous, that means there can't be any 'jumps' or discontinuities - if it starts out at a y value of 4 and then ends up at a y value of 11, it has to hit every y value in between at least once.