The image describes a scenario where students are tasked with constructing a mathematical model using functions based on a real-life situation at a computer shop. The key details of the scenario are:

• The computer shop charges 30 pesos for the first two hours.
• For every succeeding hour, an additional charge of 20 pesos is added.

Now, based on the questions:

1. What is the given?

   • a. 30 pesos for the first two hours.
   • b. 20 pesos for each succeeding hour.

2. Write the number sentence: This could refer to creating an equation or mathematical expression for the total cost $C$ in terms of the number of hours $h$:

   \begin{cases} 30, & \text{if } 0 \leq h \leq 2 \\ 30 + 20(h - 2), & \text{if } h > 2 \end{cases}$$ This function captures that the first two hours cost 30 pesos, and for every hour beyond two, an additional 20 pesos is added.

3. Write the intervals: This refers to specifying the time intervals for the charges:

   • a. For the first two hours: $0 \leq h \leq 2$
   • b. For hours after two: $h > 2$

Would you like further clarification or more detailed explanations?

Here are 5 related questions to deepen understanding:

1. How would the equation change if the shop charged differently for the first hour?
2. What happens to the cost if the customer uses the computer for exactly 3 hours?
3. Can you express the total cost as a linear function if the minimum time is more than 2 hours?
4. How would this function change if the shop introduced a flat-rate option after a certain number of hours?
5. How does the piecewise function reflect the different pricing strategies?

Tip: Understanding piecewise functions helps model scenarios where different rules apply in different situations, like pricing schemes.