To solve this problem, we need to derive an equation that accurately represents the shipping cost as a function of [tex]$x$[/tex], where [tex]$x$[/tex] is the weight of the box in pounds.
### Step-by-Step Solution:
1. Understand the Components of Cost:
- There is a flat packing fee of [tex]$5 which does not change regardless of the weight of the box.
- There is an additional charge of $[/tex]2.25 for every pound that the box weighs.
2. Express the Total Cost:
- The total cost for shipping a box will be the sum of the flat packing fee and the weight-dependent fee.
3. Form the Equation:
- Let [tex]$x$[/tex] represent the weight of the box in pounds.
- The cost due to the weight alone would be [tex]$2.25 \times x$[/tex].
- Adding the flat packing fee of [tex]$5, the total shipping cost can be represented as:
\[
f(x) = 2.25x + 5
\]
4. Compare with the Given Options:
- Option 1: \( f(x) = 2.25x + 5 \)
- Option 2: \( f(x) = 5x + 2.25 \)
- Option 3: \( f(x) = 2.25x - 5 \)
- Option 4: \( f(x) = 5x - 2.25 \)
5. Determine the Correct Equation:
- The flat fee is added to the per-pound cost, which matches Option 1: \( f(x) = 2.25x + 5 \).
Therefore, the equation that correctly represents the shipping cost as a function of $[/tex]x$ is:
[tex]\[
f(x) = 2.25x + 5
\][/tex]
The correct option is the first one.
