The Intermediate Value Property and Discontinuity - 
It’s often stated in mathematics classrooms that the graph of a continuous function can be drawn without the chalk ever leaving the chalkboard. This description also seems to characterize the graph of a function that satisfy the intermediate value property. You may recall that a function \(f\) has the intermediate value property (IVP) if for \(a < b\), all real numbers between \(f(a)\) and \(f(b)\) are attained by \(f\) on the interval \([a, b]\). We know from calculus that any continuous function has the IVP, but surprisingly these two concepts are far from equivalent. In this talk we’ll discuss functions that have the IVP, concentrating on the discontinuous ones. We’ll also provide lots of examples. Since this talk concerns functions and derivatives, students who are new to math program are particularly encouraged to attend!