The worksheet contains two word problems involving piecewise functions. Let's solve them one by one.

Problem 1:

Taxi Fare Calculation: The fare structure for the taxi service is as follows:

• Base fare (for the first 2 kilometers): ₱40.
• Additional fare (for kilometers beyond 2 km but up to 10 km): ₱15 per kilometer.
• Long-distance fare (for kilometers beyond 10 km): ₱12 per kilometer.

Question: If a passenger travels 12 kilometers, what is the total fare? Show your solution using a piecewise function.

To solve this, let's break down the distance and calculate the fare for each segment:

• Base fare (first 2 km): ₱40.
• Distance from 2 km to 10 km (8 kilometers):
  ₱15 per kilometer × 8 kilometers = ₱120.
• Distance from 10 km to 12 km (2 kilometers):
  ₱12 per kilometer × 2 kilometers = ₱24.

So, the total fare is: $\text{Total fare} = 40 + 120 + 24 = ₱184.$

Problem 2:

Mobile Data Plan Charge: The pricing structure for the mobile data plan is:

• Up to 1 GB: Free.
• 1 GB to 5 GB: ₱50 per GB.
• Above 5 GB: ₱75 per GB.

Question: If a customer uses 7 GB of data, what is the total charge? Show your solution using a piecewise function.

To solve this, let's break down the usage:

• First 1 GB: Free.
• Usage from 1 GB to 5 GB (4 GB):
  ₱50 per GB × 4 GB = ₱200.
• Usage from 5 GB to 7 GB (2 GB):
  ₱75 per GB × 2 GB = ₱150.

So, the total charge is: $\text{Total charge} = 200 + 150 = ₱350.$

Would you like further details or explanations on these solutions?

Here are 5 related questions to further explore:

1. How would the taxi fare change for a 15 km trip?
2. What is the fare if the taxi ride covers exactly 10 km?
3. How much would the customer pay for using 3 GB of data?
4. How can the piecewise function for the taxi fare be written mathematically?
5. How would you modify the mobile plan pricing if the rate for data beyond 10 GB changed?

Tip: When working with piecewise functions, always break the problem down by analyzing the range each piece of the function applies to, and apply the corresponding rate or rule.