Answer:
The answer to your problem is, A polynomial together with the absolute value function.
Explanation:
If you recall a sufficient number of specified points, a polynomial can make a pretty good model of almost any smooth function just like the picture you provided. Our function's derivative is undefined at a couple of points, so there are some options for those. If the slopes match on either side of those zeros, then the absolute value function can be used to model the "reflection" at the x-axis. Or known as, a piecewise description can be used.
The left portion of the curve looks a little like a sine wave ( a since wave is a curve representing periodic oscillations of constant amplitude as given by a sine function. ), but a cubic or other polynomial can model that wave fairly well. The portion to the right of the maximum looks like a bouncing ball ( like gravity pulls it down to earth goes up and down but goes down more and more until it reaches the floor ), so can be modeled by a piecewise quadratic function.
Thus the answer to your problem is, A polynomial together with the absolute value function.