Question

An online clothing company that does not offer any free items charges a shipping fee of $8 for orders under $25 $4 for orders between $25 and $49.99 and no shipping fee for orders of $50 or more the following piecewise function shows total cost for a shipment

Answer 1

To represent the total cost of a shipment from the online clothing company as a piecewise function, we consider both the cost of the items ordered and the applicable shipping fee based on the order total. Let's denote the total cost of the items (before shipping) as \( x \). The piecewise function for total cost \( C(x) \) can be defined as follows:

\[
C(x) =
\begin{cases}
x + 8 & \text{if } 0 \leq x < 25 \\
x + 4 & \text{if } 25 \leq x < 50 \\
x & \text{if } x \geq 50
\end{cases}
\]

### Explanation:
- For \( 0 \leq x < 25 \): The customer pays the cost of the items \( x \) plus a shipping fee of $8.
- For \( 25 \leq x < 50 \): The customer pays the cost of the items \( x \) plus a shipping fee of $4.
- For \( x \geq 50 \): The customer pays the cost of the items \( x \) with no additional shipping fee.

This piecewise function accurately reflects the shipping costs associated with different order amounts.