Piecewise Linear Function

A piecewise function is a function that is given by different expressions on different intervals. The graph of $f(x)={\begin{cases}x^{2},&{\mbox{if}}\ x<2\\-\left(x-3\right)^{2}+9,&{\mbox{if}}\ x\geq 2\end{cases}}$ is shown on the right. The open circle indicates that the point is not included on the graph and the closed circle indicates that the point is included on the graph. So $f(2)$ = 8 not 4.

$\lim _{x\to \infty }$