Chapter 1.4, Problem 55AYU

Federal Income Tax Two $2017$ Tax Rate Schedules are given in the accompanying table. If $x$ equal taxable income and $y$ equals that tax, construct a function $y=f(x)$ fir Schedule $X$.

$\begin{array}{|cccccccccccc|}\hline & & & & 2017& \text{Tax Rate }& & & & & & \\ & & \text{Schedules}& X-& \text{Single}& & & \text{Schedules}& Y-1-& \text{Married}& FillingJoinlyorQualifiedWidow(er)& \\ \begin{array}{c}\text{If Taxable }\\ \text{Income is}\\ \text{Over}\end{array}& \begin{array}{c}\text{But Not}\\ \text{Over}\end{array}& \begin{array}{c}\text{The Tax is}\\ \text{This}\\ \text{Amount}\end{array}& & \begin{array}{c}\text{Plus This }\\ \text{\%}\end{array}& \begin{array}{c}\text{Of the }\\ \text{Excess}\\ \text{Over }\end{array}& \begin{array}{c}\text{If Taxable }\\ \text{Income is}\\ \text{Over}\end{array}& \begin{array}{c}\text{But Not}\\ \text{Over}\end{array}& \begin{array}{c}\text{The Tax is}\\ \text{This}\\ \text{Amount}\end{array}& & \begin{array}{c}\text{Plus This }\\ \text{\%}\end{array}& \begin{array}{c}\text{Of the }\\ \text{Excess}\\ \text{Over }\end{array}\\ \$0& \$9,325& \$0& +& 10\%& \$0& \$0& \$18,650& \$0& +& 10\%& \$0\\ 9,325& 37,950& 932.50& +& 15\%& 9,325& 18,650& 75,900& 1,865& +& 15\%& 18,650\\ 37,950& 91,900& 5,226.25& +& 25\%& 37,950& 75,900& 153,100& 10,452.50& +& 25\%& 75,900\\ 91,900& 191,650& 18,713.75& +& 28\%& 91,900& 153,100& 233,350& 29,752.50& +& 28\%& 153,100\\ 191,650& 416,700& 46,643.75& +& 33\%& 191,650& 233,350& 416,700& 52,222.50& +& 33\%& 233,3500\\ 416,700& 418,400& 120,910.25& +& 35\%& 416,700& 416,700& 600,000& 112,728.00& +& 35\%& 416,700\\ 418,400& -& 121,505.25& +& 39.6\%& 418,400& 470,700& -& 131,628.00& +& 39.6\%& 470,700\\ \hline\end{array}$