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.
$27,000
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