1. In 2020, the Canadian government established the following federal tax rates: 15% on the first $48,535 of taxable income, + 20.5% on the next $18,535 of taxable income (on the portion of taxable income over $48,535 up to $97,069), + 26% on the next $53,404 of taxable income (on the portion of taxable income over $97,069 up to $150, 473), + 29% on the next $63,895 of taxable income (on the portion of taxable income over $150,473 up to $214.368), + 33% of taxable income over $214.368. (a) Sketch a graph representing the tax rate R(x) as a function of taxable income a. (b) Determine lim R(x) and describe what it means in context. (C) Is R() continuous everywhere? Explain. (a) Sketch a graph representing the amount of tax owed (r) as a function of taxable income. Clearly state the domain and range of this function. (e) Give the formula for the piecewise function representing the amount of tax owed (1) as a function of taxable income. (f) Is T() continuous everywhere? Explain. (g) Some people wonder if it is worth taking a raise if it bumps them into a higher tax bracket as they worry they will pay more tax than the raise is worth. Using the graph above, explain why their fears are unjustified. (h) Canada's income tax rates are called progressive because the rate increases as income increases. Suppose the government decided to apply a flat tax rate of 25% to everyone. For which income(s) would this flat rate of 25% be the same as the current progressive tax? Use a graph to explain