Question 1 / Vraag 1
Income Tax: Rates of Tax for Individuals / Inkomstebelasting: Belastingkoerse vir individue
Search on the internet (SARS website) for the rates of tax for individuals, for the 2026 tax year
(1 March 2025 - 28 February 2026). This information can be used to write income tax ( as a function
of taxable income . Use this information to create a piecewise defined function , using one
independent variable , to model the rates of tax for individuals. / Gaan soek op die internet
(SARS/SAID webtuiste) vir die belastingkoerse vir individue, vir die 2026 belastingjaar (1 Maart 2025 -
28 Februarie 2026). Hierdie inligting kan gebruik word om inkomstebelasting ( ) as ’ n funksie van die
belasbare inkomste te skryf. Gebruik hierdie inligting om ’ stuksgewys gedefinieerde funksie te
ontwikkel, deur een onafhanklike veranderlike te gebruik, om die belastingkoerse vir individue te
modelleer.

Ask by Best Frank. in South Africa

Mar 27,2025

Question

Question 1 / Vraag 1
Income Tax: Rates of Tax for Individuals / Inkomstebelasting: Belastingkoerse vir individue
Search on the internet (SARS website) for the rates of tax for individuals, for the 2026 tax year
(1 March 2025 - 28 February 2026). This information can be used to write income tax ( as a function
of taxable income . Use this information to create a piecewise defined function , using one
independent variable , to model the rates of tax for individuals. / Gaan soek op die internet
(SARS/SAID webtuiste) vir die belastingkoerse vir individue, vir die 2026 belastingjaar (1 Maart 2025 -
28 Februarie 2026). Hierdie inligting kan gebruik word om inkomstebelasting ( ) as ’ n funksie van die
belasbare inkomste te skryf. Gebruik hierdie inligting om ’ stuksgewys gedefinieerde funksie te
ontwikkel, deur een onafhanklike veranderlike te gebruik, om die belastingkoerse vir individue te
modelleer.

Ask by Best Frank. in South Africa

Mar 27,2025

UpStudy AI · Accepted Answer

To create a piecewise defined function $$ T $$ for income tax based on the rates for individuals for the 2026 tax year, we first need to gather the relevant tax rates from the SARS (South African Revenue Service) website. Since I cannot browse the internet, I will guide you on how to structure the piecewise function once you have the tax rates. ### Steps to Create the Piecewise Function: 1. **Gather Tax Rates**: Visit the SARS website and find the income tax rates for individuals for the 2026 tax year (1 March 2025 - 28 February 2026). Look for the tax brackets and corresponding rates. 2. **Define the Tax Brackets**: The tax rates are usually structured in brackets. For example, you might find something like: - 0% for income up to a certain amount - 18% for income above that amount up to another threshold - 26% for income above the next threshold, and so on. 3. **Create the Piecewise Function**: Based on the tax brackets you find, you can define the function $$ T(x) $$ as follows: $$ T(x) = \begin{cases} 0 & \text{if } x \leq a_1 \ 0.18(x - a_1) + b_1 & \text{if } a_1 < x \leq a_2 \ 0.26(x - a_2) + b_2 & \text{if } a_2 < x \leq a_3 \ \vdots & \vdots \ 0.45(x - a_n) + b_n & \text{if } x > a_n \end{cases} $$ Here, $$ a_1, a_2, \ldots, a_n $$ are the income thresholds, and $$ b_1, b_2, \ldots, b_n $$ are the tax amounts calculated at those thresholds. 4. **Example Structure**: If you find the following hypothetical tax brackets: - 0% for income up to R 200,000 - 18% for income from R 200,001 to R 350,000 - 26% for income from R 350,001 to R 500,000 - 31% for income from R 500,001 to R 750,000 - 36% for income above R 750,000 Your piecewise function might look like this: $$ T(x) = \begin{cases} 0 & \text{if } x \leq 200000 \ 0.18(x - 200000) & \text{if } 200000 < x \leq 350000 \ 0.26(x - 350000) + \text{(tax at R 350,000)} & \text{if } 350000 < x \leq 500000 \ 0.31(x - 500000) + \text{(tax at R 500,000)} & \text{if } 500000 < x \leq 750000 \ 0.36(x - 750000) + \text{(tax at R 750,000)} & \text{if } x > 750000 \end{cases} $$ 5. **Finalizing the Function**: Once you have the actual tax rates and thresholds, replace the placeholders in the piecewise function with the correct values. ### Conclusion After gathering the necessary information from the SARS website, you can construct the piecewise function $$ T(x) $$ to model the income tax rates for individuals for the specified tax year. If you provide the specific tax brackets and rates, I can help you format the function accordingly. To model the income tax rates for individuals in the 2026 tax year, create a piecewise function $$ T(x) $$ based on the tax brackets and rates found on the SARS website. Define different tax rates for each income bracket and use the function to calculate the tax based on the taxable income $$ x $$.

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