State income tax. Table $6$ shows state income tax rates for individuals filing a return in Louisiana.

$($A$)$ Write a piecewise definition for $T(x),$ the tax due on a taxable income of $x$ dollars.

$($B$)$ Graph $T(x).$

$($C$)$ Find the tax due on a taxable income of $$32,000.$ Of $$64,000.$

$($D$)$ Would it be better for a married couple in Louisiana with two equal incomes to file jointly or separately? Discuss.

Table $6$ Lovisiana State Income Tax

Single, married filing separately, or head of household:

$\backslash$table$[[$Over$,$But not over,Tax due is$],[$$$0,$$$12,500,2\%$ of taxable income$],[$$$12,500,$$$50,000,$$$250$ plus $4\%$ of excess$],[$over $$12,500,,],[$$$50,000,,\backslash$table$[[$$$1,750$ plus $6\%$ of excess$],[$over $$50,000$