erin512 2 years ago A local store owner pays her employees time-and-a-half for overtime. That means if an employee works more than 40 hours per week, the store will pay him 1.5 times his regular hourly wage of \$6.50

1. erin512

Write and graph a piecewise function that illustrates an employee's weekly pay, W, as a function of the number of hours, h, that employee works.

2. erin512

having some trouble with this, if somebody could explain how i could solve this i would really appreciate it!

3. Hero

f(x) = 6.50x, x <=40 f(x) = 260 + 9.75x, x > 40 Sorry, that's the best I can do.

4. Hero

That's not really it, but it's close

5. erin512

thanks, i got this does this seem to make sense or is this wrong? P = {0 h<0 6.5 h 0≤h≤40 260+9.75 40<h≤168}

6. Hero

But you still need a variable for the the third interval.

7. Hero

The problem is, you need a variable that will represent h > 40 because it won't be the same as 0 < h < 40

8. Hero

for h > 40, it is overtime so it starts back at 1 again.

9. Hero

For instance, if she works one hour overtime, it won't be 260 + 9.75(41) it will be 260 + 9.75(1) For two hours, it will be 260 + 9.75(2) so the variable cannot be h. It has to be "o" maybe for overtime hours. But we have to write a piecewise function in terms of the same variable, so good luck with that.

10. Hero

I figured it out.

11. Hero

For the 3rd interval, you have to find the equation of the line. So use points (40, 260) and (41, 269.75) to find the slope, then re-write the equation of the line in terms of h.

12. erin512

oh okay thank you soo much, what would the equation be in that case?

13. erin512

@Hero

14. Hero

wait

15. Hero

f(h) = 9.75h - 130

16. Hero

Tricky problem, but not impossible to figure out

17. Hero

so f(h) = 6.50h 0 < h < 40 f(h) = 9.75h - 130 h > 40

18. erin512

@Hero thank you so much, i understand much better now. do you know how i could graph that?

19. erin512

never mind i got it :)