Example 1: Create a Piecewise Function for candy pricing at Wal-Mart.

Problem Analysis:

We are tasked with creating a piecewise function to represent the cost of buying bags of Snickers at Wal-Mart. The pricing structure is as follows:
- If you buy fewer than 4 bags, each bag costs $3.45.
- If you buy 4 or more bags, each bag costs $3.00.

Step-by-Step Solution:

#### 1. Define the Variables:
Let:
- \( x \) = the number of bags of Snickers purchased.
- \( C(x) \) = the total cost of purchasing \( x \) bags of Snickers.

#### 2. Identify the Conditions:
The problem specifies two different pricing rules based on the number of bags purchased:
- For \( x < 4 \): Each bag costs $3.45.
- For \( x \geq 4 \): Each bag costs $3.00.

#### 3. Formulate the Piecewise Function:
The total cost \( C(x) \) depends on the number of bags \( x \). We can write the piecewise function as follows:

\[
C(x) =
\begin{cases}
3.45x & \text{if } x < 4 \\
3.00x & \text{if } x \geq 4
\end{cases}
\]

#### Explanation of the Function:
- For \( x < 4 \): If you buy fewer than 4 bags, the cost per bag is $3.45. Therefore, the total cost is \( 3.45 \times x \).
- For \( x \geq 4 \): If you buy 4 or more bags, the cost per bag is $3.00. Therefore, the total cost is \( 3.00 \times x \).

#### 4. Verify the Function:
- If \( x = 3 \) (fewer than 4 bags):
\[
C(3) = 3.45 \times 3 = 10.35
\]
This matches the condition for \( x < 4 \).

- If \( x = 4 \) (4 or more bags):
\[
C(4) = 3.00 \times 4 = 12.00
\]
This matches the condition for \( x \geq 4 \).

- If \( x = 5 \) (4 or more bags):
\[
C(5) = 3.00 \times 5 = 15.00
\]
This also matches the condition for \( x \geq 4 \).

#### Final Answer:
The piecewise function that represents the cost of the bags of Snickers is:

\[
\boxed{C(x) =
\begin{cases}
3.45x & \text{if } x < 4 \\
3.00x & \text{if } x \geq 4
\end{cases}}
\]