How do I write a piecewise function?

Question

There is a new wireless company named Math-Mobile who has an interesting talk plan available:
• For a flat fee of $15 you get a phone number plus 75 anytime minutes
• For minutes 76 through 150, the additional cost is $.05 per minute
• For minutes 151 through 250, the additional cost is $.15 per minute
• For every minute past 250, the additional cost is $.10 per minute

Construct a piecewise function modeling the monthly pre-tax/fees bill.

Answer 1

A piecewise function is a function that contains different relationship under certain intervals of the independent variable.

 

Let G(x) represent the plan.

Let m represent the minutes.

 

G(x) =   {  15                 ,     0 ≤ m ≤ 75

                 0.05m + 15   ,   76 ≤ m ≤ 150

                 0.15m + 15   ,   151 ≤ m ≤ 250

                 0.10m + 15   ,   m > 250          }