To determine which function best represents the cost [tex]\( C \)[/tex] for [tex]\( x \)[/tex] pages of photocopies, we need to examine the pricing structure given:
1. The shop charges [tex]$0.60 per page for orders of less than or equal to 30 pages.
2. The shop charges $[/tex]0.50 per page for orders of 31 to 60 pages.
3. The shop charges $0.40 per page for orders of more than 60 pages.
Let's break it down step by step:
1. For orders of [tex]\( 0 < x \leq 30 \)[/tex] pages, the cost [tex]\( C \)[/tex] is given by:
[tex]\[
C(x) = 0.60x
\][/tex]
2. For orders of [tex]\( 31 \leq x \leq 60 \)[/tex] pages, the cost [tex]\( C \)[/tex] is given by:
[tex]\[
C(x) = 0.50x
\][/tex]
3. For orders of [tex]\( x > 61 \)[/tex] pages, the cost [tex]\( C \)[/tex] is given by:
[tex]\[
C(x) = 0.40x
\][/tex]
Considering these points, the correct function to represent the cost [tex]\( C \)[/tex] for [tex]\( x \)[/tex] pages of photocopies is:
[tex]\[
C(x) = \left\{
\begin{array}{ll}
0.60x & \text{if } 0 < x \leq 30 \\
0.50x & \text{if } 31 \leq x \leq 60 \\
0.40x & \text{if } x > 61
\end{array}
\right.
\][/tex]
Thus, the function that best represents the cost for [tex]\( x \)[/tex] pages of photocopies is the third function listed:
[tex]\[
C(x) = \left\{
\begin{array}{ll}
0.60x & \text{if } 0 < x \leq 30 \\
0.50x & \text{if } 31 < x \leq 60 \\
0.40x & \text{if } x > 61
\end{array}
\right.
\][/tex]
