Question

You have a summer job that pays time and a half for overtime. that is if you work more than 40 hours per week,your hourly wage for the extra hours is 1.5 times your normal hourly wage is $7. What is the domain for you typical 40 hour work week?

Answer 1

Your pay is described by a piecewise function p(t) where t is hours worked.
$p(t)=\left\{\begin{array}{rcl}7t&\mbox{for}&t\leq40\\10.5t-140&\mbox{for}&t>40\end{array}\right.$

The domain of this function is the number of hours you can work in a week—zero to 168. This problem, however, is asking for the domain for a typical 40-hour week. That will be the interval [0, 40].