In Makati City, income tax is 3.5% on the first P10,000 of income or less, and 5% on any income in excess of $10,000. Let the tax Ts) be a function of the income s.

Given the information, let's define the tax function $ T(s) $ for the income $ s $ in Makati City. The tax rate structure is as follows:

1. For the first P10,000 or less, the income tax is 3.5%.
2. For income exceeding P10,000, the tax on the excess income is 5%.

The tax function $ T(s) $ can be defined piecewise as follows:

- **Case 1:** If $ s \leq 10,000 $:
  \[
  T(s) = 0.035 \times s
  \]
- **Case 2:** If $ s > 10,000 $:
  \[
  T(s) = 0.035 \times 10,000 + 0.05 \times (s - 10,000)
  \]

This represents the total tax $ T(s) $ on an income $ s $ based on the given tax rates.

### Explanation:

- For incomes up to P10,000, the tax is simply 3.5% of the income.
- For incomes greater than P10,000, the tax includes 3.5% of the first P10,000 (which is $ 0.035 \times 10,000 $ = P350), plus 5% on any income exceeding P10,000.

Would you like a detailed example calculation for a specific income?

### Related Questions:

1. How much tax would be paid on an income of P12,000?
2. What is the tax on an income of P8,000?
3. How would the tax change if the rate for the excess income was increased to 6%?
4. Can you represent this tax function graphically for a range of incomes?
5. How does this piecewise function behave for very large incomes?

### Tip:
Piecewise functions are often used to model real-world scenarios where different conditions apply to different intervals of the input.

Learn how to compute income tax in Makati City using piecewise functions. Understand the tax structure where income tax is 3.5% on the first P10,000 or less and 5% on any income exceeding P10,000. Includes detailed examples and explanations.

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