A$)$ In the US we have different tax rate structures for different types of filers, such as individual, married filing jointly, etc. The $2022$ US income tax brackets for a "head of household" filer are found below. Complete the table below. Use the table above as an example, and round to whole numbers in your solutions. $(10$ points$)$

$\backslash$table$[[$Income Level,$\backslash$table$[[$Tax$],[$Rate$]],\backslash$table$[[$Max Amount of Income at this$],[$Tax Rate$]],\backslash$table$[[$Max Amount$],[$of Tax$]]],[$Up to $$14,650,10\%,,],[$Between $$14,651$ and $$55,900,12\%,,],[$Between $$55,901$ and $$89,050,22\%,,],[$Between $$89,051$ and $$170,050,24\%,,],[$Between $$170,051$ and $$215,950,32\%,,],[$Between $$215,951$ and $$539,900,35\%,,],[5539,900,37\%,,]]$

B$)$ Write a piecewise$-$defined function that models the $2022$ head of household tax brackets where $x$ is the annual income for the filer and $f(x)$ is the amount of tax owed. Use the example piecewise function to guide your work. $(12$ points$)$