Financial Algebra© Cengage/South-Western Slide 11

7-2

MODELING TAX SCHEDULES

Construct income tax graphs using compound equations.

OBJECTIVES

Financial Algebra© Cengage Learning/South-Western Slide 22

flat taxproportional taxprogressive tax system tax bracketregressive tax schedule

Key Terms

Financial Algebra© Cengage Learning/South-Western Slide 33

Write the tax schedule notation, interval notation, and compound inequality notation that would apply to an income of $172,876.99.

Example 1Example 1

Financial Algebra© Cengage Learning/South-Western Slide 44

Tax EquationTax EquationTax EquationTax Equation

{)(xf

70035770035735077096

70035730020030020033082844

30020045013145013128055025

4501311006510065250509628

1006505016050161506051

050160100

, ),(.,,, ),(.,,, ),(.,

,, ),(..,,, ),(.,

, .

xx

xx

xx

xx

xx

xx

Financial Algebra© Cengage Learning/South-Western Slide 55

How does the piecewise function relate to the tax computation worksheet?

Example 2Example 2

Financial Algebra© Cengage Learning/South-Western Slide 66

Express the equation in the married taxpayers filing jointly schedule in y = mx + b form to determine the tax for an income of $46,000.

Example 3Example 3

Financial Algebra© Cengage Learning/South-Western Slide 77

Examine the piecewise function f(x) composed of the first three equations in Example 3.

f(x) =

0.10x 0 < x ≤ 16,050

0.15x − 802.5 16,050 < x ≤ 65,100

0.25x − 7,312.5 65,100 < x ≤ 131,450

Graph the function on the appropriate interval.

Example 4Example 4

Financial Algebra© Cengage Learning/South-Western Slide 88

If you were to graph the fourth equation in the piecewise function, y = 0.28x − 11,256, where would you expect the last point in that equation to be? Explain your reasoning.

CHECK YOUR UNDERSTANDING

Financial Algebra© Cengage Learning/South-Western Slide 99

What are the monetary implications of the fact that the slope of the last segment of the piecewise function is greater than the slope of the segment preceding it?

EXTEND YOUR UNDERSTANDING