The $2020$ U$.$S$.$ federal income tax is a function of taxable income. Write T$($x$)$ for

the tax owed on a taxable income of x dollars. For tax year $2020$ the function T for a single

taxpayer was specified as follows:

$1$

If your taxable

income was over...

$$0$

But not

over $...$

Your tax is$...$

Of the amount

over...

$$9,875$

$10\%$

$$0$

$$9,875$

$$40,125$

$$987\mathrm{.}50+12\%$

$$9,875$

$$40,125$

$$85,525$

$$4,617\mathrm{.}50+22\%$

$$40,125$

$$85,525$

$$163,000$ $$14,605\mathrm{.}50+24\%$

$$85,525$

$$163,000$

$$207,350$ $$33,199\mathrm{.}50+32\%$

$$163,000$

$$207,350$

$$47,391\mathrm{.}50+35\%$

$$207,350$

Hint: FIRST PLUG IN SOME NUMBERS. Compute the tax owed, if the income is $10$K$,$

$15$K$,20$K$,50$K$,60$K$.$ Then write the formula.

$($a$)$ Compute the tax owed by a single taxpayer on a taxable income of $$96,300.$

$($b$)$ Compute the tax owed by a single taxpayer on a taxable income of $$10,100.$

$($c$)$ Represent T as a piecewise$-$defined function of income x