Question

a telephone company offers a monthly cellular phone plan for $35.00. it includes 350 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. $c(x)=\begin{cases}35.00& \text{if }0leq xleq350\\35.00 + 0.25(x - 350)&\text{if }x>350end{cases}$ fill in the simplified expression below $c(x)=\begin{cases}35.00& \text{if }0leq xleq350\square&\text{if }x>350end{cases}$ (use integers or decimals for any numbers in the expression. do not factor.)

Explanation:

Step1: Expand the expression

\[

$$\begin{align*} 35.00 + 0.25(x - 350)&=35.00+0.25x-0.25\times350\\ &=35.00 + 0.25x-87.5 \end{align*}$$

\]

Step2: Combine like - terms

\[35.00-87.5 + 0.25x=-52.5+0.25x\]

Answer:

\[C(x)=

$$\begin{cases}35.00&\text{if }0\leq x\leq350\\- 52.5+0.25x&\text{if }x > 350\end{cases}$$

\]