how to write a piecewise function application

Question

you have a job where you make $10 per hour

after you work 40 hours you get payed time and one half

you may only work a max of 60 hours

write a piecewise function that represents your pay for up to 60 hours

Answer 1

Let, X be a number of hours, then we have

10 * X, for 0 < X <= 40

15 * ( X - 40) + 400, for 40 < X <= 60

Answer 2

So with a piecewise function, the behavior of the function can change on different intervals. For instance we can have a straight line with a slope of 2 from ×=0 to x=4, then the slope can increase or decrease from x=4 to x=8. This means that unlike other functions, we may need multiple equations to represent the piecewise function.

For this problem, we know that our initial slope is found from the information "$10 for every 1 hour worked. This means that when x increases by 1 (hours) y increases by 10.

Then when x= 40, our slope changes. The worker now makes time and a half, which means we multiple the initial hourly rate ($10) by 1.5

We get $10(1.5) = $15.

So now we know that from x=0 to x=40, the slope is 10. So at x=0, y=0 and at x=40, y = 400.

Then on the next interval from x=40 to x=60 (the problem tells us that this is the maximum amount of hours the individual can work) the slope is 15. So the graph goes from y=400 when x= 40 to when x =60, y= 400+ 20(15) or from the point: 40,400 to the point 60, 700.