Maria earns a net taxable income of ₱8,000,000 annually. According to the tax bracket she falls under, her income tax is calculated as ₱490,000 plus 32% of the amount exceeding ₱2,000,000.
Piecewise function of this

To represent Maria's income tax calculation as a piecewise function, we'll break down the income tax formula in relation to the income thresholds provided.

The tax bracket tells us:
- For any income above ₱2,000,000, the tax is ₱490,000 plus 32% of the excess over ₱2,000,000.

We can express this as a piecewise function for \( x \), where \( x \) is Maria's net taxable income.

\[
T(x) =
\begin{cases} 
0, & 0 \leq x \leq 2,000,000 \\
490,000 + 0.32(x - 2,000,000), & x > 2,000,000
\end{cases}
\]

### Explanation:
- For income \( x \leq 2,000,000 \), the tax is zero because no information is provided for income below ₱2,000,000.
- For income \( x > 2,000,000 \), the tax starts at ₱490,000 and an additional 32% of the amount exceeding ₱2,000,000 is added.

For Maria, her income is ₱8,000,000. Plugging this into the function:

\[
T(8,000,000) = 490,000 + 0.32(8,000,000 - 2,000,000)
\]
\[
T(8,000,000) = 490,000 + 0.32(6,000,000)
\]
\[
T(8,000,000) = 490,000 + 1,920,000 = 2,410,000
\]

Her total income tax is ₱2,410,000.

Would you like more details or have any questions?

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Here are 5 related questions for further exploration:
1. How does the tax rate affect income levels below ₱2,000,000 in other brackets?
2. What would be the income tax if Maria earned ₱5,000,000 annually?
3. How can you generalize this piecewise function for other tax brackets?
4. What if the tax rate for income above ₱2,000,000 changed to 35%?
5. How would you calculate the net income after tax if Maria's income changes?

**Tip:** Piecewise functions are a great tool for representing situations where a rule changes depending on the value of the input, such as tax brackets!

Maria earns a net taxable income of ₱8,000,000 annually. According to the tax bracket she falls under, her income tax is calculated as ₱490,000 plus 32% of the amount exceeding ₱2,000,000. Piecewise function of this.

Explore how to calculate income tax for ₱8,000,000 using a piecewise function. The problem breaks down tax brackets, including a base tax of ₱490,000 and 32% for income exceeding ₱2,000,000. Learn the step-by-step solution and apply percentage calculations for finance students.

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