Chapter 5.1, Problem 2P

In each of Problems $1$ through $4$, sketch the graph of the given function. In each case, determine whether $f$ is continuous, piecewise continuous, or neither on the interval $0\le t\le 3$.

$f(t)=\{\begin{array}{l}\sin \left(\pi t\right),0\le t\le 1\\ {\left(t-1\right)}^{-1},1<t\le 2\\ 1,2<t\le 3\end{array}$