Ican’t get this problem for ab calculus

  (A)  1.

Step-by-step explanation:

The intermediate value theorem (IVT) tells you that if you have a continuous function with two different y-values on some interval, somewhere in that interval, the function will have a value between those two y-values.

Consider the attached diagram. If we have f(-1) = 7 and f(1) = 3, we want to choose a "k" such that f(0) = k will mean that the function must cross y = 3/2 at least twice. Clearly, any value of k below 3/2 will make that happen. The only answer choice meeting that requirement is choice A.

___

A continuous function does not have to be linear, but may be. It can have any number of wiggles, so there may be multiple crossings of any given y-value in the interval. Shown are a couple of straight lines, which cross the given y-value only once in each sub-interval. The point of the IVT is that there must be at least one crossing if the function is continuous.