Question

a telephone company offers a monthly cellular phone plan for $30.00. it includes 350 free minutes plus $0.20 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}30.00& \text{if }0leq xleq350\\30.00 + 0.20(x - 350)&\text{if }x>350end{cases}
fill in the simplified expression below.
c(x)=\begin{cases}30.00& \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

When $x > 350$, expand $30.00+0.20(x - 350)$. Use the distributive property $a(b - c)=ab - ac$, where $a = 0.20$, $b=x$ and $c = 350$. So $30.00+0.20(x - 350)=30.00+0.20x-0.20\times350$.

Step2: Calculate the constant term

Calculate $0.20\times350 = 70$. Then $30.00+0.20x-70=0.20x - 40$.

Answer:

$C(x)=

$$\begin{cases}30.00& \text{if }0\leq x\leq350\\0.20x - 40& \text{if }x > 350\end{cases}$$

$