Question

a telephone company offers a monthly cellular phone plan for $25.00. it includes 300 free minutes plus $0.25 per minute for additional minutes. the following function gives the monthly cost for a subscriber, where x is the number of minutes used. simplify the expression in the second - line of the piece - wise function. then use point - plotting to graph the function.
c(x)=\begin{cases}25.00& \text{if }0leq xleq300\\25.00 + 0.25(x - 300)&\text{if }x>300end{cases}
fill in the simplified expression below.
c(x)=\begin{cases}25.00& \text{if }0leq xleq300\square&\text{if }x>300end{cases}
(use integers or decimals for any numbers in the expression. do not factor.)

Explanation:

Step1: Expand the second - part of the function

\[

$$\begin{align*} 25.00+0.25(x - 300)&=25.00+0.25x-0.25\times300\\ &=25.00 + 0.25x-75\\ &=0.25x - 50 \end{align*}$$

\]

Answer:

\[C(x)=

$$\begin{cases}25.00& \text{if }0\leq x\leq300\\0.25x - 50& \text{if }x > 300\end{cases}$$

\]