Is it true that for all functions f, if a0, then there must be a number c, with a

Question

Is it true that for all functions f, if a<b, f(a)<0, f(b)>0, then there must be a number c, with a<c<b and f(c)=0?

Keith L. · Accepted Answer

The statement is true for all continuous functions.

Is it true that for all functions f, if a<b, f(a)<0, f(b)>0, then there must be a number c, with a<c<b and f(c)=0?