Question

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. Write a function o(x) that defines the hourly pay for overtime hours worked.

Answer 1

i confused

Answer 2

was the other one wrong?

Answer 3

I am sorry, I am not good at this.....time and a half for 8.75 =13.13
f(x) = 13.13(x)
time and a half for 8.75 = 13.13 per overtime hour

Answer 4

you might better get a second opinion.....

Answer 5

at least your trying to help, but how did u get 13.13?

Answer 6

time and a half for 8.75 = 1.5 x 8.75 = 13.125 rounded to 13.13

Answer 7

oh wait...it is 8.50....let me change it

Answer 8

i think u where right the first time with 12.75

Answer 9

f(x) = 12.75(x)
12.75 is time and a half for 8.50
I guess I was ...lol

Answer 10

are you sure about this one?

Answer 11

I think so.....you still might need a second opinion....what do you think ?

Answer 12

do u know how to write a piecewise function? I'll ask just in case.

Answer 13

lol.....no sorry....not good at functions

Answer 14

me either.

Answer 15

we're told to "Write a function o(x) that defines the hourly pay for overtime hours worked."

so because overtime only kicks in when you work "more than 40 hours per week", this means that x > 40

Answer 16

the overtime pay is "1.5 times the regular hourly wage of $8.50"

so the overtime hourly pay is 1.5*8.5 = 12.75 dollars an hour

Answer 17

so u multiply 1.5 and 8.5.

Answer 18

so if x is some number over 40, then x - 40 is the number of hours you work overtime (eg: if x = 50, then x-40 = 50 - 40 = 10 and you worked 10 overtime hours)


so if you want to figure out how much overtime you earn, you just multiply the two to get

12.75(x-40)

optionally you can distribute, but it's fine to leave it like that

Answer 19

got it. do u know how to write a piecewise function?

Answer 20

yes I do

Answer 21

can u help me with this question? combine the two function you just wrote to form a piewise function, W(x), in which each function is defined for a specific domain. so H(x)=8.5x and O(x)=12.75(x-40)

Answer 22

a piecewise function is just a combination of two or more functions

Answer 23

what you do is basically write all the functions in one column

next to each function, you describe the conditions or restrictions on each piece of that piecewise function

Answer 24

i dont now how to organize the function.

Answer 25

so say f(x) is the piecewise function

Answer 26

we would then say

f(x) = 8.5x if x<= 40

OR

f(x) = 12.75(x-40) if x>40

Answer 27

notice how x dictates which function to use

if x <= 40, then you use the first piece

if x > 40, then you go for the second piece

you can only use one piece at a time

Answer 28

so it doesnt have to do with greater or less.

Answer 29

you would then combine the two and write it in this notation