Chapter 2.4, Problem 55AYU

Federal Income Tax Two 2018 Tax Rate Schedules are given in the accompanying table. If $x$ equals taxable income and y equals the tax due, construct a function $y=f(x)$ for Scheduled $X$.

$\begin{array}{c}\text{2018}\text{Tax}\text{Rate}\\ \begin{array}{cccccccccccc}& \text{Schedule}& X& -& \text{Single}& & \text{Schedule}& \text{Y-1-Married}& \text{Filing}& \text{Jointly}\text{or}& \text{Qualified}& \text{Widow(er)}\\ \begin{array}{l}\text{If}\text{Taxable}\\ \text{Income}\text{is}\\ \text{Over}\end{array}& \begin{array}{l}\text{But}\text{Not}\\ \text{Over}\end{array}& \begin{array}{l}\text{The}\text{Tax}\text{is}\\ \text{This}\\ \text{Amount}\end{array}& & \begin{array}{l}\text{Plus}\\ \text{this}\text{\%}\end{array}& \begin{array}{l}Ofthe\\ Excess\\ Over\end{array}& \begin{array}{l}\text{If}\text{Taxable}\\ \text{Income}\text{is}\\ \text{Over}\end{array}& \begin{array}{l}\text{But}\text{Not}\\ \text{Over}\end{array}& \begin{array}{l}\text{The}\text{Tax}\text{is}\\ \text{This}\\ \text{Amount}\end{array}& & \begin{array}{l}\text{Plus}\\ \text{this}\text{\%}\end{array}& \begin{array}{l}Ofthe\\ Excess\\ Over\end{array}\\ \$0& \$9,525& \$0& +& 10\%& \$0& \$0& \$19,050& \$0& +& 10\%& \$0\\ 9,525& 38,700& 952.50& +& 12\%& 9,525& 19,050& 77,400& 1,905& +& 12\%& 19,050\\ 38,700& 82,500& 4,453.50& +& 22\%& 38,700& 77,400& 165,000& 8,907.00& +& 22\%& 77,400\\ 82,500& 157,500& 14,089.50& +& 24\%& 82,500& 165,000& 315,000& 28,179.00& +& 24\%& 165,000\\ 157,500& 200,000& 32,089.50& +& 32\%& 157,500& 315,000& 400,000& 64,179.00& +& 32\%& 315,000\\ 200,000& 500,000& 45,689.50& +& 35\%& 200,000& 400,000& 600,000& 91,379.00& +& 35\%& 400,000\\ 500,000& -& 150,689.50& +& 37\%& 500,000& 600,000& -& 161,379.00& +& 37\%& 600,000\end{array}\end{array}$