Piecewise-defined function

[Rusho]

A phone company offers a deal by which a long distance phone call costs .99 cents for the first 20 minutes and .07 per minute thereafter. Write a piecewise-defined function for the cost C of making a phone call that lasts x minutes.

So I did this:


f(x) { .99(6) 0<= x
.99(20) 0=> x >= 20

Not a clue what I'm doing...

 

[VietDao29]

Okay, say you make a x-minute phone call (x <= 20), i.e a phone call that lasts no longer than 20 minutes. How much will you have to pay if you know that each minute costs you .99 cents?
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If you make a y-minute phone call (y > 20), i.e a phone call that lasts more than 20 minutes. How much will you have to pay for the first 20 minutes? How much will you have to pay for the (y - 20) minutes last? Then do you know how much will you have to pay for that whole y-minute phone call?
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Your function will look like this:
$$f(x) := \left\{ \begin{array}{l} ... , \quad \quad \mbox{if } 0 \leq x \leq 20 \\ ... , \quad \quad \mbox{if } x > 20 \end{array} \right.$$
Can you go from here? :)

 

[Architeuthis Dux]

I would like to clarify and provide a more accurate piecewise-defined function for the cost C of making a phone call that lasts x minutes:

C(x) = { 0.99x for 0 <= x < 20
{ 0.99(20) + 0.07(x-20) for x >= 20

This function represents the cost C of a phone call that lasts x minutes, where the first 20 minutes cost $0.99 and any additional minutes cost $0.07 per minute. The first part of the function (0.99x) covers the cost for calls that are less than 20 minutes, while the second part (0.99(20) + 0.07(x-20)) covers the cost for calls that are 20 minutes or longer.

It is important to note that the first part of the function has a strict inequality (less than) while the second part has an inclusive inequality (greater than or equal to). This is because the first 20 minutes are charged at a different rate than any additional minutes.

I hope this clarifies the concept of a piecewise-defined function and its application in this scenario.