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Let's go through both activities from the image you uploaded:

### **Activity 1: Rational Function**
You are asked to represent the rational function:

\[
f(x) = \frac{x^2 - 3x - 10}{x}
\]

- You need to use a table of values and then plot a graph based on the table, connecting the points.
- The range of integer values for \(x\) is given as \(-6 \leq x \leq 10\), with the restriction that \(x \neq 0\) (since division by zero is undefined).
- To begin, calculate the function \(f(x)\) for each integer value of \(x\) between -6 and 10, excluding zero. Then, use those points to plot the graph.

**To help you start:**
- First, simplify \(f(x)\):
\[
f(x) = \frac{x^2 - 3x - 10}{x} = x - 3 - \frac{10}{x}
\]
This gives us a clear expression to calculate values for different \(x\).

### **Activity 2: Basketball Problem**
The team from Barangay Culiat has won 12 out of 25 games, which gives them a winning percentage of 48%. The task asks you to determine their winning percentage after certain outcomes.

- **Winning percentage formula:**
\[
\text{Winning percentage} = \frac{\text{Total wins}}{\text{Total games}} \times 100
\]

Let’s calculate their new winning percentages based on the given scenarios:

1. **If they win 10 games in a row:**
   They will have played 35 games (25 + 10) and won 22 games (12 + 10). So, calculate the percentage based on 22 wins out of 35 games.
   
2. **For other values (15, 20, 30, 50, and 100 games):** 
   Apply the same formula and increase both the number of wins and games played accordingly.

3. **Can they reach a 100% winning percentage?**
   This would mean they need to win every single game after a certain point, so consider if it is feasible.

Would you like me to work out the table of values for **Activity 1** and the percentages for **Activity 2** in more detail?

### Follow-up Questions:
1. Would you like me to calculate specific values for \(f(x)\) between -6 and 10?
2. Do you need help plotting the graph for the rational function?
3. Should I compute the winning percentages for each of the cases (10, 15, 20 games, etc.)?
4. Do you need clarification on the calculation of a winning percentage?
5. Would you like a step-by-step breakdown of solving each of these activities?

**Tip:** When graphing a rational function, check for vertical asymptotes (like at \(x = 0\) here) and how the function behaves as \(x\) approaches these points.

Activity 1: Represent the rational function f(x) = (x^2 - 3x - 10)/x using a table of values and plot a graph of the function by connecting points. Taking function values integers in -6 ≤ x ≤ 10, x ≠ 0.

Activity 2: In an inter-barangay basketball league, the team from Barangay Culiat has won 12 out of 25 games, a winning percentage of 48%. What will be their winning percentage if they win: a) 10 games in a row? b) 15? 20? 30? 50? 100 games? c) Can they reach a 100% winning percentage?

Learn how to represent the rational function f(x) = (x^2 - 3x - 10)/x using a table of values and graph it by connecting points. Also, explore winning percentage calculations for various game scenarios. Suitable for Grades 9-12 students interested in graphing rational functions and calculating percentages.

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