Chapter 2.2, Problem 74E

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

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

(b) Graph $T\left(x\right)$.

(c) Find the tax due on a taxable income of $\text{\$32,000}$. Of $\text{\$64,000}$

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