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 range 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. The range is the set of values p(t) can take on, which we have said is p(0) to p(168). This problem, however, is asking for the range for a typical 40-hour week. That will be p(0) to p(40): the interval [0, 280].