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Based on the image you provided, the table shows the tax schedule for different annual salary brackets and their corresponding tax rules. Let me break this down and formulate a function rule for each bracket:

### Tax Brackets (Personal Income Tax Schedule 2018–2022):

1. **For annual salary not over ₱250,000**:
   - **Tax**: 0% (i.e., no tax)
   - **Function rule**: \( T(x) = 0 \) for \( x \leq 250,000 \)
   
2. **For annual salary over ₱250,000 but not over ₱400,000**:
   - **Tax**: 15% of the excess over ₱250,000
   - **Function rule**: \( T(x) = 0.15(x - 250,000) \) for \( 250,000 < x \leq 400,000 \)
   
3. **For annual salary over ₱400,000 but not over ₱800,000**:
   - **Tax**: ₱22,500 + 20% of the excess over ₱400,000
   - **Function rule**: \( T(x) = 22,500 + 0.20(x - 400,000) \) for \( 400,000 < x \leq 800,000 \)
   
4. **For annual salary over ₱800,000 but not over ₱2 Million**:
   - **Tax**: ₱102,500 + 25% of the excess over ₱800,000
   - **Function rule**: \( T(x) = 102,500 + 0.25(x - 800,000) \) for \( 800,000 < x \leq 2,000,000 \)
   
5. **For annual salary over ₱2 Million but not over ₱8 Million**:
   - **Tax**: ₱402,500 + 30% of the excess over ₱2 Million
   - **Function rule**: \( T(x) = 402,500 + 0.30(x - 2,000,000) \) for \( 2,000,000 < x \leq 8,000,000 \)
   
6. **For annual salary over ₱8 Million**:
   - **Tax**: ₱2,202,500 + 35% of the excess over ₱8 Million
   - **Function rule**: \( T(x) = 2,202,500 + 0.35(x - 8,000,000) \) for \( x > 8,000,000 \)

### Generalized Function Rule:
If we denote the annual salary as \( x \), the overall tax function \( T(x) \) would be piecewise, covering different intervals:

\[
T(x) = 
\begin{cases} 
0 & \text{for } x \leq 250,000 \\
0.15(x - 250,000) & \text{for } 250,000 < x \leq 400,000 \\
22,500 + 0.20(x - 400,000) & \text{for } 400,000 < x \leq 800,000 \\
102,500 + 0.25(x - 800,000) & \text{for } 800,000 < x \leq 2,000,000 \\
402,500 + 0.30(x - 2,000,000) & \text{for } 2,000,000 < x \leq 8,000,000 \\
2,202,500 + 0.35(x - 8,000,000) & \text{for } x > 8,000,000
\end{cases}
\]

### Do you want more details or have any questions?

### 5 Related Questions:
1. How is the income tax rate for each bracket determined mathematically?
2. How does the excess over a certain amount affect the tax calculation in each bracket?
3. Can you compute the tax for a specific salary, say ₱600,000 or ₱3,500,000?
4. What happens when a salary crosses multiple brackets, how is the total tax calculated?
5. How does the tax rate progression compare to a flat tax rate system?

### Tip:
Always ensure that you apply the correct rule for the correct income bracket to avoid calculation errors, especially when the salary lies near the boundary of two tax brackets.

Generate a function rule from the provided personal income tax table.

Explore the detailed function rule for calculating personal income tax based on the 2018-2022 tax schedule in the Philippines. This guide covers the piecewise function for different income brackets, suitable for understanding tax computations.

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