We claim that Schedule Y-l defines a function, call it f, of income x, for x ≥ 0. Indeed,...

We claim that Schedule Y-l defines a function, call it f, of income x, for x ≥ 0. Indeed, for any x ≥ 0, x belongs to exactly one of the intervals

and as soon as the interval is determined, there is a single rule that applies to compute a unique value f(x).

 For example, to compute f(83,500), tax on an income of $83,500, observe first that 83,500 belongs to the interval (65, 100, 131,450] and for such an x the tax formula is f(x) = 8,962.50 + 0.25(x − 65,100), since x − 65,100 is the amount over $65,100 and it is taxed at the rate 25% = 0.25.

Therefore,

 To illustrate further, we write out the entire Schedule Y-1 in our generic notation for a case-defined function.

With these formulas, we can geometrically depict the income tax function, as in Figure 1.

FIGURE 1

Income tax function.

Use the preceding income tax function f to determine the tax on the given taxable income in the year 2008.

$560,000