Theorem: CCD.IVT.0: If $f$ is a continuous function on the interval
$[a,b]$ and $0$ is between $f(a)$ and $f(b)$ or $f(a) \cdot f(b) < 0$, then there is a number $c \in [a,b]$
where $f(c) = 0$. Theorem: CCD.IVT: If $f$ is a continuous function on the interval $[a,b]$ and $v$ is between $f(a)$ and $f(b)$, then there is a number $c \in [a,b]$ where $f(c) = v$ For the mapping diagram visualization of IVT.0, the continuity of the function $f$ can be interpreted as the function representing the position of an object at varying times between times $a$ and $b$. The assumption that $0$ is between $f(a)$ and $f(b)$ is interpreted that between times $a$ and $b$ the object has moved either from a negative to a positive position or vice versa.The conclusion is interpreted that at some time, $c$, the object's position is precisely $0$, i.e., $f(c)=0$. Not only do mapping diagrams provide a distinct alternative to the graphical visualization of the intermediate value theorem, they also provide a sensible alternative visualization of the proof of IVT.0 by the Bisection Method. 
Mapping Diagram for IVT.0

Proof Outline and Visualization of CCD.IVT.0 using the "bisection
method." 