Question

Tracy has a cell phone plan that provides 250 free minutes each month for a

flat rate of $29. For any minutes over 250, Tracy is charged $0.35 per minute.
Which of the following piecewise functions represents charges based on
Tracy's cell phone plan?
29,45 250 1
O A. f(x) =
| 35x,x > 250)
B. f(x)=
29.x < 250
129+ 35x, x > 250)
O C. f(x)={ 29, x>250
129+. 35x, x5 250
29,7 $250
O D. f(x) =
129+.35(x-250),x > 250)

Answer 1

`f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {29+0.35(x-250)\,\,for \,x>250}} \right.`

Explanation:

If we call "x" the number of call minutes used with this plan, the piecewise function used to describe it must represent;

a) a constant value of 29 for any x value smaller than or equal to 250

b) a line with positive slope of 0.35 for the region with x larger than 250. The mathematical representation of such increasing straight line, should be given by a line of slope m = 0.35, and containing the point (250, 29) which is the starting point for this right hand side portion of the domain:

`f(x)=0.35(x-250)+29\\f(x)=0.35 x-87.5+29\\f(x)=0.35 x-58.5`

So the function should look like:

`f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {29+0.35(x-250)\,\,for \,x>250}} \right.`

or as shown above, in a more simplified form:

`f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {0.35x-58.5\,\,\,for \,\,x>250}} \right.`