The piecewise function for this should be [tex] f(x) \left \{ {{y = 20x, x < 42} \atop {y = 28x + 840, x > 42}} \right. [/tex].
We can find the first equation simply. He gets 20 every hour up to 42 hours. Therefore, the function gives us our first equation of y = 20x when x < 42.
The second one, we must know what the base amount he would make before starting to make 28 an hour. The 28 an hour would be 28x, but he would have already made 840 before hand. Which we can determine by multiplying the base of 42 hrs by 20.
42 * 20 = 840.
