The fictitious state of aribraska has a graduated state income tax. residents pay 3% on the first $15,000 of income. the next $25,000 earned is taxed at a rate of 5%. any money earned above $40,000 is taxed at 7%. the income tax for aribraska is modeled by a piecewise defined function. over which part of the domain is the piecewise function defined as f(x) = 0.05x – 300?

Your answer choice is correct: the range 15,000–40,000

Step-by-step explanation:

Above income of 15,000 and below income of 40,000, the problem statement tells us the tax rate is 5%. If income amount is represented by x, then .05x is the amount of the tax (subject to the credits offered by the graduated scale). The term 0.05x in the question tells you the applicable range is 15,000 ≤ x ≤ 40,000.

If 15,000 were taxed at the 5% rate, the tax amount would be $750. Instead, the tax amount on that income is 3% of 15,000, or $450—a tax that is $300 less than 0.05x. Hence in the range 15,000–40,000, the tax computation is ...

... f(x) = 0.05x -300 . . . . . for 15,000 ≤ x ≤ 40,000

Above 40,000

At the middle income tax rate, $40,000 would have a tax of ...

... 0.05×40000 -300 = 1700

At 7%, $40,000 would have a tax of

... 0.07×40000 = 2800

Then the actual tax on amounts above $40,000 is $1100 less than 7% of the income.

... f(x) = 0.07x -1100 . . . . . for x ≥ 40,000

for income 15,000 is less than or equal to x is less than or equal to 40,000.

SO B

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