Math 124
Names:
Below is the 2006 Tax rate Schedule for people filing as “single.” Let X represent your
taxable income.
Schedule X — Single
If taxable income is over--
But not over--
The tax is:
$0
$7,550
10% of the amount over $0
$7,550
$30,650
$755 plus 15% of the amount over 7,550
$30,650
$74,200
$4,220.00 plus 25% of the amount over 30,650
$74,200
$154,800
$15,107.50 plus 28% of the amount over 74,200
$154,800
$336,550
$37,675.50 plus 33% of the amount over 154,800
$336,550
no limit
$97,653.00 plus 35% of the amount over 336,550
1. Find the amount of taxes T, due as a function of X. (This will be a piecewise defined
function.)
2. Using your function, find T(7,500), T(30,650) and T(74,200).
3. Find the limit as x approaches 7,500, the limit as x approaches 30,650 and the limit as
x approaches 74,200.
4. Is this a continuous function?
5. Now find a function describing your Take home income: (taxable income – tax).
6. Is this a continuous function? Justify your answer.
7. Is it possible that a raise at work can leave you with less take-home income?