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The problem outlines a rental pricing structure based on the number of days the car is rented. Let's break it down:

- For the first 3 days, the rate is ₱5000 per day.
- From the 4th to the 6th day, the rate is ₱4000 per day.
- From the 7th day onwards, the rate is ₱3500 per day.

Now, we need to represent the rental cost function \( r(d) \), where \( d \) is the number of days the car is rented.

### Defining the function \( r(d) \):

\[
r(d) =
\begin{cases}
5000d, & \text{if } d \leq 3 \\
15000 + 4000(d - 3), & \text{if } 4 \leq d \leq 6 \\
27000 + 3500(d - 6), & \text{if } d \geq 7
\end{cases}
\]

#### Explanation:
- For \( d \leq 3 \), it's simply \( 5000 \times d \), since the rate is constant at ₱5000 per day.
- For \( 4 \leq d \leq 6 \), the total cost for the first 3 days is ₱15000, and the cost for any additional day is ₱4000.
- For \( d \geq 7 \), the cost for the first 6 days is ₱27000, and the cost for any additional day beyond that is ₱3500.

Would you like to go over the calculation with specific examples, or do you have any other questions?

Here are 5 related questions for further practice:
1. What is the cost if a customer rents the car for 5 days?
2. How much does it cost if the car is rented for 8 days?
3. Represent the total cost function graphically for \( r(d) \).
4. How much would a customer pay if they rent the car for 10 days?
5. If the rate for more than 7 days was changed to ₱3000 per day, how would the function \( r(d) \) change?

**Tip:** Breaking a problem into intervals helps to construct piecewise functions more efficiently.

A car rental agency charges customers based on the number of days they rent a car. The pricing structure is as follows: For the first three days, the daily rate is ₱5000. After the third day, the daily rate reduces to ₱4000 per day. If a customer rents a car for seven or more days, they receive a discount, and the daily rate becomes ₱3500 per day. Represent the rental cost based on the provided pricing structure using the function r(d), where d is the number of days the car is rented.

Learn how to calculate the cost of renting a car using a piecewise function. The problem breaks down different daily rates based on the number of days rented, offering a practical application of algebra. Suitable for students in Grades 9-12.

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