Question

write a piece - wise function that models the cellular phone billing plan described below. let x represent the number of minutes used and c(x) represent the cost for those x minutes. then graph the function: $25.00 per month buys 350 minutes. additional time costs $0.20 per minute. choose the correct graph of the function.

Explanation:

Step1: Define cost for $x\leq350$

For $0\leq x\leq350$, the cost $C(x)$ is a fixed - rate of $\$25$. So, $C(x)=25$ when $0\leq x\leq350$.

Step2: Define cost for $x > 350$

For $x>350$, the cost is the base - rate of $\$25$ plus $\$0.20$ per minute for the minutes over 350. The number of minutes over 350 is $(x - 350)$. So, $C(x)=25+0.2(x - 350)=25 + 0.2x-70=0.2x - 45$ when $x>350$.
The piece - wise function is $C(x)=

$$\begin{cases}25, &0\leq x\leq350\\0.2x - 45, &x>350\end{cases}$$

$

To graph:

• For $0\leq x\leq350$, the graph is a horizontal line at $y = 25$.
• For $x>350$, when $x = 351$, $C(351)=25+0.2\times(351 - 350)=25 + 0.2=25.2$. The slope of the line for $x>350$ is $m = 0.2$.

The graph starts as a horizontal line at $y = 25$ from $x = 0$ to $x = 350$ and then has a positive - slope of $0.2$ for $x>350$.

Looking at the options, we need to find a graph that has a horizontal line segment at $y = 25$ from $x = 0$ to $x = 350$ and then a line with a positive slope starting at $x=350$.

Answer:

The correct graph depends on the specific visual characteristics of the options, but it should have a horizontal line $y = 25$ for $0\leq x\leq350$ and then a line with slope $0.2$ for $x>350$. Without seeing the exact details of the graphs in options A, B, C, and D, we can't pick a specific letter - option, but the described graph behavior is what to look for.