Quadrant 1 of a coordinate plane shows the x axis labeled taxable income and the y axis labeled tax rate.

A tax preparer needs to explain tax rates to a client. Which of the following best interprets the piecewise linear function for a tax client who earns $54,000?

(1 point)
Responses

The client will be taxed at a rate of 24% since their taxable income is within the third step of the function.
The client will be taxed at a rate of 24% since their taxable income is within the third step of the function.

The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $28,375, which is the amount of taxable income within the second step. The remaining $16,350 will be taxed at a rate of 25%.
The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $28,375, which is the amount of taxable income within the second step. The remaining $16,350 will be taxed at a rate of 25%.

The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $37,650. They will be taxed at a rate of 25% for $54,000.
The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $37,650. They will be taxed at a rate of 25% for $54,000.

The client will be taxed at a rate of 25% since their taxable income is within the third step of the function.

1 answer

To interpret the piecewise linear function for a client who earns $54,000, we need to understand how the progressive tax system works. Typically, in a progressive tax system, different portions of income are taxed at different rates.

Given the options provided, let’s analyze the income brackets usually associated with a progressive tax system:

  1. 10% for the first portion of taxable income (e.g., up to $9,275).
  2. 15% for the next portion (e.g., from $9,276 to $38,650).
  3. 25% for taxable income over that amount.

For an income of $54,000, the application would be as follows:

  • The first $9,275 would be taxed at 10%.
  • The amount from $9,276 to $38,650 (which is $28,375) would be taxed at 15%.
  • The remaining amount over $38,650 up to $54,000 (which is $15,350) would be taxed at 25%.

Thus, the best response interpreting the piecewise tax function would be: The client will be taxed at a rate of 10% for the first $9,275 of taxable income. They will be taxed at a rate of 15% for $28,375, which is the amount of taxable income within the second step. The remaining $15,350 will be taxed at a rate of 25%.

However, the correct option provided specifically mentions $16,350 for the 25% bracket, which is slightly incorrect based on the breakdown, but the general approach of the provided options does help a client understand how their income is taxed progressively.

Therefore, choose the response that expresses the understanding of how the tax brackets work with the provided figures.