Determine the domain of each piece. Domain of piece 1:[
)

Domain of piece 2: [
)

Domain of piece 3:[
]

On a coordinate plane, line 1 goes from (negative 4, 4) to (negative 1, 1), line 2 goes from (negative 1, 1) to (1, 1), and line 3 goes from (1, 1) to (5, negative 3).

  8.  Tax in 10% tax bracket: $927.50

  9.  Amount of taxable income at 10%: $9275.00

  10.  Total income tax: $4846.25

  11.  Tax in 15% bracket: $3918.75

  12.  Amount of taxable income at 15%: $26,125

Step-by-step explanation:

This set of questions is presented in an unfortunate order. You actually have to answer later questions before you can answer earlier ones.

The goal is to compute the tax on a taxable income of $35,400 based on the given tax rate table. Doing this proceeds in several steps:

Each tax bracket has an upper limit of income. Income above that limit is taxed at a higher rate. The first step is to figure out how much of the taxable income fits in any particular tax bracket.

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The taxable income is given as $35,400, and filing status is given as Single, so only the table columns under Single are applicable. This income amount exceeds the upper limit of the 10% bracket ($9,275), so only $9,275 is taxed at 10%. (This is the answer to question 9.)

The tax on that amount is ...

  10% · $9275 = $927.50 . . . . . the answer to question 8

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The first $9,275 of income fills the 10% bracket. Any taxable income amount above that, but less than $37,650, is taxed at the rate of the next bracket, 15%. The amount that falls into the 15% bracket is ...

  $35,400 - 9,275 = $26,125 . . . . . the answer to question "12"

The tax on this amount is ...

  15% · $26,125 = $3918.75 . . . . . the answer to question 11

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Now, we know the tax owed on income amounts in each tax bracket, so we can add them up to find the total tax owed:

  tax in 10% bracket + tax in 15% bracket = total tax owed

  $927.50 + 3,918.75 = $4,846.25 . . . . . . the answer to question 10

Comment on the problem

You are given an earnings amount and asked to compute the tax on it. In general, exemptions and deductions are applied to earnings to arrive at a taxable income amount. That step has been omitted in this problem.

In practice, this sort of tax table likely would not be used. Rather, the amount of tax due on $35,400 would be computed using a simpler formula: 0.15 · $35,400 - 463.75 = $4,846.25. This requires only one multiplication and one addition, instead of the one multiplication and one addition required for each tax bracket using the method in the problem sequence.

In practice, too, the final amount of tax owed is rounded to the nearest dollar, so would be $4,846.