Consider the following function:

$f(t)=\{\begin{array}{cc}(t-7{)}^2,& 0t<mn>8</mn>\\ 2,& 8t17\\ \frac{2}{17}t,& t>17\end{array}$

Which of these properties does $f$ satisfy? Select all that apply.

$f$ is piecewise continuous on $[0,).$

${\displaystyle \underset{0}{\overset{}{}}}{e}^{-st}f(t)dt$ diverges.

The Laplace transform of $f$ exists.

$f$ is continuous on $[0,).$

$f$ is of exponential order.

Question $2$