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.

\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? --- 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!