Post on 15-Dec-2015
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