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Schedule $Y-1,$ to be used by married tax payers in 2003 is given in Table 2 Letting $x$ be your taxable income and $t$ be your tax, find $t=T(x)$ for the domain $0 < x \leq 311,950$ and plot its graph.

$$T(x)=\left\{\begin{array}{cc}0.10 x & 0<x \leq 14,000 \\0.15 x-700 & 14,000<x \leq 56,800 \\0.25 x-6,380 & 56,800<x \leq 114,650 \\0.28 x-9,819.50 & 114,650<x \leq 174,700 \\0.33 x-18,554.50 & 174,700<x \leq 311,950 \\0.35 x-24,793.50 & x>311,950\end{array}\right.$$

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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01:25

Graph the indicated functi…

00:40

Here is the 2011 Federal T…

00:41

02:15

Table 5 shows a recent sta…

01:06

Use the 2000 tax schedule …

03:02

Federal Income Tax Refer t…

03:11

Federal Income Tax Two 201…

piece wise functions are useful in determining the amount of taxes someone must pay. Given a tax schedule. Here we have a tax schedule given for incomes between zero on 311,950. I've giving us a little snippet of it, just about half of it. So our incomes are actually here, going from 0 to 114,000 to 650 just for simplicity. And to avoid the repetition off, filling out this piece wise function because it does get to be a little bit of work. As we keep going here, we can just follow our general function written in blue. The quotations just indicate which column we're working with, the values for which were filling this in. And we can start with the first one by simply just just filling. In the general function, we have 0.1 times x minus 14,000 plus zero. That is, if our X is greater than zero, but less than or equal to 14,000. Our next line would be 0.15 times x minus 56 1008 100 plus 1400. And that is if ex falls between 56,800 and 14,000, and then we have 0.25 times X minus 114,650 plus 7820. And that is if our income falls between 56,800 and 114,650. So that right here, written in red, is our peace flies function. Given the tax schedule directly above it, you can see how it gets a little bit repetitive as we keep going to. If your tax schedule was even larger than this with more rose, you would just repeat this process for each one individually, and that would give you your tax schedule.

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