Chapter 1.1, Problem 59E

Income Taxes The U.S. federal income tax is a function of taxable income. Write $T\left(x\right)$ for the tax owed on a taxable income of x dollars. For tax year 2015 the function T for a single taxpayer was specified as follows:

If your taxable income was over …	But not over …	Your tax is …	Of the amount over…
$0	9,225	10%	$0
9,225	37,450	$922.50 + 15%	$9,225
37,450	90,750	5,156.25 + 25%	$37,450
90,750	189,300	18,481.25 + 28%	$90,750
189,300	411,500	46,075.25 + 33%	$189,300
411,500	413,200	119,401.25 + 35%	$411,500
413,200	–	119,996.25 + 39.6%	$413,200

a. Represent T as a piecewise-defined function of income x. [HINT: Each row of the table defines a formula with a condition]

b. Use your function to compute the tax owed by a single taxpayer on a taxable income of $45,000.