Question

1. Sprint PCS offers a monthly cellular phone plan for $39.99. It includes 450 anytime minutes and charges $.45 per minute for additional minutes. a. x represents __________________ (2 points) b. f(x) represents ___________________ (2 points) c. Write out your piecewise function, including the domain.

Answer 1

`f(x) = \left \{ {{39.99; 0 \le x \le 450} \atop {0.45x - 162.51; \ x>450}} \right.`

Explanation:

Given

Charges: $39.99 for first 450 minutes

Charges: $0.45 for additional minutes

(a): What is x

x represents the total minutes

(b): What is f(x)

f(x) represents the total monthly cellular charges

(c): The piecewise function

For the first 450 minutes, the function is:

`f(x) = 39.99;\ 0 \le x \le 450`

For additional minutes.

In (a), the total minutes is x.

So, we have:

Total Charges = Charges for first 450 minutes + Charges for additional minutes * (Minutes after 450 minutes)

`Total\ Charges = 39.99 + 0.45 * (x - 450)`

`f(x) = 39.99 + 0.45 * (x - 450)`

Open bracket

`f(x) = 39.99 + 0.45x - 0.45 * 450`

`f(x) = 39.99 + 0.45x - 202.5`

Collect Like Terms

`f(x) = 0.45x+39.99 - 202.5`

`f(x) = 0.45x-162.51`

The range of the above function is: x > 450.

So, the piecewise function is:

`f(x) = \left \{ {{39.99; 0 \le x \le 450} \atop {0.45x - 162.51; \ x>450}} \right.`