Let's analyze the conditions given for determining the total cost of trout for Karen's seafood restaurant.
1. If Karen orders less than 10 pounds of trout:
- Each pound costs \[tex]$28.
- There is an additional shipping fee of \$[/tex]4.
- Thus, the total cost [tex]\( C \)[/tex] for [tex]\( x \)[/tex] pounds when [tex]\( 0 < x < 10 \)[/tex] is given by:
[tex]\[
C = 28x + 4
\][/tex]
2. If Karen orders 10 pounds or more of trout:
- Each pound costs \[tex]$22.
- There is an additional shipping fee of \$[/tex]8.
- Thus, the total cost [tex]\( C \)[/tex] for [tex]\( x \)[/tex] pounds when [tex]\( x \geq 10 \)[/tex] is given by:
[tex]\[
C = 22x + 8
\][/tex]
We need to construct the piecewise function [tex]\( f(x) \)[/tex] based on these conditions.
The correct piecewise function is:
[tex]\[
f(x) =
\begin{cases}
28x + 4 & \text{if } 0 < x < 10 \\
22x + 8 & \text{if } x \geq 10
\end{cases}
\][/tex]
Comparing this with the options provided, we see that option B matches the conditions exactly:
[tex]\[
f(x) =
\begin{cases}
28x + 4 & \text{if } 0 < x < 10 \\
22x + 8 & \text{if } x \geq 10
\end{cases}
\][/tex]
Thus, the correct answer is:
[tex]\[
B
\][/tex]
