Consider the following simplified version of the actual Arizona state tax tables, for single people taxable incomes up to $53,000. For 2020, a single person whose taxable income is between $0-$26,500 is charged 2.59% in tax. A single person whose taxable income is between $26,501-$53,000 is charged 2.59% of the first $26,500, and 3.34 % of the amount over $26,500. Write a piecewise-linear function to represent the AZ state income tax for a single taxpayer as a function of taxable income, for taxable incomes up to $53,000. Note that these are referred to as tax brackets. The actual tax brackets for the state of AZ in 2020 are given in the table below:

Single

Tax Rate Income Range Taxes Due

2.59% $0-$26,500 2.59% within Bracket

3.34% $26,501-$53,000 3.34% within Bracket

4.17% $53,001-$159,000 4.17% within Bracket

4.50% $159,001 + 4.50% on income over $159,000

Part a) Create a table of at least eight values and write a simplified piecewise linear function to represent the AZ State income tax for a single person as a function of taxable income, but only for taxable incomes of up to $53,000.

Part b) In 2020, how much tax does someone in Arizona filing as a single person owe if they have a taxable income of $38,000? Round to the nearest cent.

Part c) If a single person paid $876.70 in taxes in 2020, what was their income? If a single person paid $642.32 in taxes in 2020, what was their income?