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Question 425942: Hi, Im having trouble coming up with an equation for this problem. Can someone help.
You pay a certain long distance rate that depends on your number of minutes talked. If you talk from 1 to 700 minutes, you pay 20 cents a minute. If you talk 701 to 1500 minutes, you pay 12 cents a minute. If you talk anything over 1500 minutes, you pay 8 cents a minute.
a. Is the number of minutes you talk a function of your long distance rate?
b. Is your long distance rate a function of the number of minutes you talk?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! talk 0 to 700 minutes = .20 per min
talk 70-1500 minutes = .12 per min
talk over 1500 minutes = .08 per min
these are essentially 3 different functions.
1 function for 0 to 700 minutes
1 function for 701 to 1500 minutes
1 function for over 1500 minutes.
we only have to pick one of them to answer the question.
let's pick 0 to 700 minutes.
let y = the number of minutes you talk.
let x = your long distance rate.
we make y = f(x) which means that the number of minutes you talk is a function of your long distance rate.
the definition of a function is that, for each x, there is one and only one unique y.
this rule is violated because for each x, you have up to 700 minutes that you can call.
each x gets you multiple y's so the definition of a function is not preserved.
in this case, we have to say that y <> f(x).
y would be called a relation of x. the variable y is definitely related to the value of x, but it's not a function because it violates one of the rules of a function.
so, the number of minutes that you call is definitely not a function of the long distance rate.
now let's look at the long distance rate being a function of the minutes that you call.
let y = your long distance rate.
let x = the number of minutes that you talk.
we make y = f(x) which means that your long distance rate is a function of the number of minutes that you call.
for each x, there is only 1 rate that will apply.
for 1 to 700 minutes, you will pay .2*x
for 701 to 1500 minutes, you will pay .12*x
for over 1500 minutes, you will pay .08*x
each x only gets you only 1 y so the definition of a function is preserved.
i believe that's the gist of what this problem is trying to get you to understand.
as far as a formula is concerned, your formula would be called a piecewise function in that the rules for relating x to y would change depending on the value of x.
essentially, you have 3 formulas.
they are:
y = .2*x for 0 <=x <= 700
y = .12*x for 700 < x <= 1500
y = .08*x for x > 1500
each of these formulas is a separate function that is used within the domain of x specified.
a good reference that talks about this is shown below:
http://www.cliffsnotes.com/study_guide/Relations-vs-Functions.topicArticleId-10792,articleId-10775.html
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