The limit of a piecewise-defined function

Instructions
Slide the (black) cluster point to learn how the values of the funcion [math]f\left(x\right)[/math] behave around it.[br]2. Slide both, [math]x_{left}[/math] and [math]x_{right}[/math] towards the cluster point to learn what are the [i]side-limits [/i](provided that they exist)[i].[/i]

Information: The limit of a piecewise-defined function