7 2 MODELING TAX SCHEDULES OBJECTIVES Construct income

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

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

Example 1 Write the tax schedule notation, interval notation, and compound inequality notation that would apply to an income of $172, 876. 99. Slide 3 Financial Algebra © Cengage Learning/South-Western

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

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

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

Example 4 Examine the piecewise function f(x) composed of the first three equations in Example 3. f(x) = 0. 10 x 16, 050 0. 15 x − 802. 5 65, 100 0<x≤ 16, 050 < x ≤ 0. 25 x − 7, 312. 5 65, 100 < x ≤ 131, 450 Graph the function on the appropriate interval. Slide 7 Financial Algebra © Cengage Learning/South-Western

CHECK YOUR UNDERSTANDING 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. Slide 8 Financial Algebra © Cengage Learning/South-Western

EXTEND YOUR UNDERSTANDING 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? Slide 9 Financial Algebra © Cengage Learning/South-Western