Question

Piecewise functions help?

Answer 1

A local store owner pays her employees time-and-a-half for overtime. That means for every hour an employee works more than 40 hours per week, the store will pay 1.5 times the regular hourly wage of $8.50.

Part I: Write a piecewise function that defines the hourly wage for employees. Be sure to include pieces for employees who work 40 hours a week or less, and for employees who work more than 40 hours.

Answer 2

\[f(x) = \left\{ \left(\begin{matrix}8.5x, 0<x<40 \\ 12.75x, x>40\end{matrix}\right) \right\}\]

Here is my answer (ignore the parenthesis. The signs in the top line should be "greater than OR EQUAL TO". Did I do it correctly?

Answer 3

\[\large f(x)=\cases{8.5x,\qquad 0\le x\le40\\ 12.75x,\qquad x>40}\]Yes, good :)

Answer 4

Yes, exactly.
Now, the second part of the question is what I'm a little unsure about.
Part II: Graph a piecewise function that illustrates an employee's hourly pay, W, as a function of the number of hours, h, that employee works.

Answer 5

Would the graph be a horizontal line at y = 8.5 from 0-40 along the x-axis, jumping to 12.75 after it reaches 40? Or... would I graph y = 8.5x as a line and then increase the slope when it hits 40?

Answer 6

Yes, the latter.
Diagonal line y=8.5x, then steeper line later on.

Answer 7

Perfect, thanks. Now Part III:
Determine how much an employee will be paid if he or she were to work 55 hours in a week.
Would the equation be: 8.5(40) + 12.75(15) ?

Answer 8

Yes. Which now I realize we screwed up the first part.
My bad my bad.

Answer 9

Do you see how it's constructed right now?
It looks like you're getting paid 12.75 for EVERY hour, including the first 40.

Answer 10

:O oh no

Answer 11

Hmm. The instructions are a bit unclear... do they only pay 12.75 for hours worked in addition to the 40?

Answer 12

Yes.
If you work 50 hours,
you don't get 50(12.75),
you get the base pay 40(8.50) and 10 hours at the bonus rate 10(12.75)

Answer 13

Can you think of a way we could write this an an equation? :d

Answer 14

Expression*

Answer 15

8.5(40) + 12.75(x) maybe? would that go inside the squigglies {} ?

Answer 16

Ooo very close!
But again, if we work 50 hours, plugging in x=50 causes a problem, ya?

Answer 17

Aha! 8.5(40) + 12.75(40 - x) eh?

Answer 18

Aha, even closer!\[\large f(x)=\cases{8.5x,\qquad\qquad\qquad\qquad\qquad\quad 0\le x\le40\\ 8.5(40)+12.75(x-40),\qquad x>40}\]

Answer 19

Awesome sauce! Thanks for catching that. Like a ninja.
Alright, for part III I would just plug 55 in for x, correct?

Answer 20

Yes, which should simplify to what you had before,
8.5(40) + 12.75(15)

Answer 21

Which would give me $531.25 as an answer? and that's what she earned in a week, right?

Answer 22

Probably...
They forgot to mention that she shadows as a drug dealer in the evenings. I think they forgot to include those hours. She's just trying to keep food on the table for her babies Bobby and Davey. It's a rough life out there. She'll make it though. Especially since John left her. It's all she can do to keep the bad thoughts from coming back... stay busy Suzy. You're gonna be ok.

Answer 23

Hmmmmm.
Can we back up a sec to part II? The graph part?
It would start at the point (0, 0) then the slope would be 8.5... the graph they gave me to plot it on doesn't fit... take a look

Answer 24

Hahaha you're wacked.

Answer 25

And delirious.

Answer 26

But hey, at least you're helpful! ;)

Answer 27

She funna git dat skrilla
@agent0smith ya meeaaan?

Answer 28

I see arrows on the sides of the graph.
Is it stretchable?

Answer 29

Look at the axis... the y-axis goes up to 15 and the x-axis goes up to 60. What the heck.

Answer 30

No lol, it's a worksheet I printed out.

Answer 31

The x-axis is a-okay. They didn't give us anything to worry about past 55 hours.

Answer 32

Then I guess you'll have to relabel the graph :)
Scribble out the 10 and write something else
like uhhh

Answer 33

This isn't for the 55 hour example, it just says:
Part II: Graph a piecewise function that illustrates an employee's hourly pay, W, as a function of the number of hours, h, that employee works.

Answer 34

For real? :O

Answer 35

I wonder sometimes about this course...

Answer 36

lol

Answer 37

8.5(40)=340 maybe that's a good value for the 10.
And then break that into 5 pieces.
So each little tick mark will be 68s.

Answer 38

Okay, done. I don't get how SOMEONE wouldn't have caught something as obvious as that though... -___-

Answer 39

:( http://www.wolframalpha.com/input/?i=f(x)+%3D+%7B8.5x,+0%3Cx%3C40;+12.75(x-40)+%2B+340,+x%3E40%7D

Answer 40

I don't know how to put a piecewise into wolfram :\
sec checking...

Answer 41

Ah, it's okay. I think I have it from here.. thanks for all the excellent help x)

Answer 42

Desmos is better :d
https://www.desmos.com/calculator/qtinxsmywi

Answer 43

Thanks zepppy ! :)

Answer 44

Dis gurl cray cray

Answer 45

I know you're not talking about me agent *raises eyebrows*

Answer 46

Ya simmer down Angel

Answer 47

Ayo CYT @Abbles, put dem eyebrows back where they belong. I'm referring to the drug dealin' gurl in the question. Her babies finna end up motherless some day.

Answer 48

Hahahahaha xD. omg I'm laughing so hard.

Answer 49

I wasn't sure CYT was okay to spell out here. The other day i got a warning for using the a** word for the human posterior.

Answer 50

Haha, probably not. I got banned the other day for supposedly posting a test question (not true, but whatever).
Out of curiosity, what math question prompted the use of a**? lol

Answer 51

I don't remember, I just know it was an entirely appropriate use of the word.