The question is incomplete, but if I had to guess, it's an exercise in using the intermediate value theorem. The IVT says that for a continuous function [tex]h(x)[/tex], there is some value of [tex]c[/tex] within any interval [tex][a,b][/tex], i.e. [tex]a<c<b[/tex], in the domain of [tex]h[/tex] such that [tex]h(a)\le h(c)\le h(b)[/tex] when [tex]h(a)<h(b)[/tex], or [tex]h(b)\le h(c)\le h(a)[/tex] when [tex]h(b)<h(a)[/tex].
We're told that [tex]h(8)=19[/tex] and [tex]h(-2)=2[/tex]. The IVT then guarantees the existence of some value of [tex]c[/tex] between -2 and 8 such that [tex]2\le h(c)\le19[/tex].
It looks like [tex]h(13)=18[/tex] is one of several possible answer choices. We can't say anything about the value of [tex]h(13)[/tex] because we only know how [tex]h[/tex] behaves between -2 and 8; the number 13 falls outside of this range. So this choice is not correct.
