A jeepney ride in Lucena costs ₱ 9.00 for the first 4 kilometers, and each
additional kilometers adds ₱0.75 to the fare. Use a piecewise function to
represent the jeepney fare F in terms of the distance d in kilometers.

To represent the jeepney fare \( F(d) \) as a piecewise function of the distance \( d \) in kilometers, we can break the fare calculation into two parts:

1. For the first 4 kilometers, the fare is a flat rate of ₱9.00.
2. For any distance beyond 4 kilometers, an additional ₱0.75 is added per kilometer.

Let's define the function \( F(d) \):

\[
F(d) =
\begin{cases} 
9.00, & \text{if } 0 \leq d \leq 4 \\
9.00 + 0.75(d - 4), & \text{if } d > 4
\end{cases}
\]

### Explanation:
- **For \( 0 \leq d \leq 4 \)**: The fare is ₱9.00 because the distance is within the first 4 kilometers.
- **For \( d > 4 \)**: The fare is ₱9.00 plus ₱0.75 for each kilometer beyond 4 kilometers. The term \( (d - 4) \) represents the number of kilometers beyond the initial 4 kilometers.

### Example:
- If \( d = 3 \) kilometers, then \( F(d) = 9.00 \) pesos.
- If \( d = 6 \) kilometers, then \( F(d) = 9.00 + 0.75(6 - 4) = 9.00 + 1.50 = 10.50 \) pesos.

Would you like to see more details or have any questions?

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**Related Questions:**
1. How would the fare change if the base fare for the first 4 kilometers increased to ₱10.00?
2. What would the fare be for a distance of 8 kilometers?
3. How does the function change if the additional fare per kilometer was ₱1.00 instead of ₱0.75?
4. How would the piecewise function look if the initial distance was 5 kilometers instead of 4?
5. How can we calculate the total fare for a trip of 15 kilometers?
6. What if there is a maximum fare cap of ₱20.00? How would the function change?
7. How would the function be affected if the fare for the first 4 kilometers was dependent on the time of day?
8. What is the mathematical significance of the point where \( d = 4 \) in this function?

**Tip:** When creating piecewise functions, it's essential to carefully define the different cases based on the conditions given, ensuring that each segment of the function applies to the correct range of inputs.

Learn how to calculate jeepney fare using a piecewise function based on distance traveled. For the first 4 kilometers, the fare is a flat rate of ₱9.00. Beyond that, an additional ₱0.75 per kilometer is added to the fare. Examples included for different distances.

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