To determine which piecewise function best models the cost [tex]\( f(x) \)[/tex] of ordering [tex]\( x \)[/tex] pounds of trout from Karen's online retailer, let's carefully analyze the problem's conditions:
1. For orders less than 10 pounds ([tex]\( 0 < x < 10 \)[/tex]):
- Each pound of trout costs \[tex]$28.
- There is a shipping fee of \$[/tex]4.
Therefore, the cost function over this interval is:
[tex]\[
f(x) = 28x + 4
\][/tex]
2. For orders of 10 pounds or more ([tex]\( x \geq 10 \)[/tex]):
- Each pound of trout costs \[tex]$22.
- There is a shipping fee of \$[/tex]8.
Thus, the cost function over this interval is:
[tex]\[
f(x) = 22x + 8
\][/tex]
Given these conditions, the appropriate piecewise function for the cost [tex]\( f(x) \)[/tex] of ordering [tex]\( x \)[/tex] pounds of trout is:
[tex]\[
f(x) = \begin{cases}
28x + 4, & \text{if } 0 < x < 10 \\
22x + 8, & \text{if } x \geq 10
\end{cases}
\][/tex]
So, the correct piecewise function is:
A. [tex]\( f(x) = \left\{ \begin{array}{ll} 28x + 4, & 0 < x < 10 \\ 22x + 8, & x \geq 10 \end{array} \right. \)[/tex]
Thus, the answer is:
[tex]\[
\boxed{1}
\][/tex]
