1. Financial Algebra © Cengage/South-Western Slide 1 7-2 MODELING TAX SCHEDULES Construct income tax graphs using compound equations. OBJECTIVES

2. Financial Algebra © Cengage Learning/South-Western Slide 2 flat tax proportional tax progressive tax system tax bracket regressive tax schedule Key Terms

3. Financial Algebra © Cengage Learning/South-Western Slide 3 Write the tax schedule notation, interval notation, and compound inequality notation that would apply to an income of $172,876.99. Example 1

4. Financial Algebra © Cengage Learning/South-Western Slide 4 Tax Equation

5. Financial Algebra © Cengage Learning/South-Western Slide 5 How does the piecewise function relate to the tax computation worksheet? Example 2

6. Financial Algebra © Cengage Learning/South-Western Slide 6 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 3

7. Financial Algebra © Cengage Learning/South-Western Slide 7 Examine the piecewise function f(x) composed of the first three equations in Example 3. f(x) = 0.10 x 0 < x ≤ 16,050 0.15 x − 802.5 16,050 < x ≤ 65,100 0.25 x − 7,312.5 65,100 < x ≤ 131,450 Graph the function on the appropriate interval. Example 4

8. Financial Algebra © Cengage Learning/South-Western Slide 8 If you were to graph the fourth equation in the piecewise function, y = 0.28 x − 11,256, where would you expect the last point in that equation to be? Explain your reasoning. CHECK YOUR UNDERSTANDING

9. Financial Algebra © Cengage Learning/South-Western Slide 9 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