To model the cellular phone billing plan described, let's define the piecewise function [tex]\( C(x) \)[/tex], where [tex]\( x \)[/tex] represents the number of minutes used and [tex]\( C(x) \)[/tex] represents the cost for those [tex]\( x \)[/tex] minutes.
Given:
1. The base monthly cost is [tex]$20.00 for up to 350 minutes.
2. Each additional minute beyond 350 minutes costs $[/tex]0.25 per minute.
We can break this into two distinct cases for the piecewise function:
1. When [tex]\( 0 \leq x \leq 350 \)[/tex]:
- In this range, the cost is just the base cost of [tex]$20.00.
2. When \( x > 350 \):
- In this range, the cost is the base cost of $[/tex]20.00 plus an additional $0.25 for each minute beyond 350.
Let's write these cases as a piecewise function:
[tex]\[
C(x) =
\begin{cases}
20.00 & \text{if } 0 \leq x \leq 350 \\
20 + 0.25(x - 350) & \text{if } x > 350
\end{cases}
\][/tex]
Here is the same piecewise function with clearly filled values:
[tex]\[
C(x) =
\begin{cases}
20.00 & \text{if } 0 \leq x \leq 350 \\
20 + 0.25(x - 350) & \text{if } x > 350
\end{cases}
\][/tex]
To graph this function:
1. Plot a horizontal line at [tex]\( y = 20 \)[/tex] from [tex]\( x = 0 \)[/tex] to [tex]\( x = 350 \)[/tex].
2. For [tex]\( x > 350 \)[/tex], the function [tex]\( 20 + 0.25(x - 350) \)[/tex] starts from the point [tex]\( (350, 20) \)[/tex] and increases linearly with a slope of 0.25.
This graph will show a horizontal line segment from [tex]\( (0, 20) \)[/tex] to [tex]\( (350, 20) \)[/tex] and then a line with a positive slope going onwards from [tex]\( (350, 20) \)[/tex].
