MATH 115 Cilli-Turner Modeling Problem #2 PIECEWISE FUNCTIONS (SECTION 3.2) STANDARD: F1 Federal and state income tax is computed within income brackets and your taxable amount (income) is separated into an amount owed in each bracket. Each of the percentages you see below is called a marginal tax rate. Each rate applies only to an amount earned that is within a particular bracket. That means that if your taxable income $45,000, you would owe 10% on the first $9,875,12% on the portion from $9,875 to $40,125 (so on a total of $30,250 ), and 22% on the portion from $40,125 to $45,000. Thus, your total tax paid would be 0.1(9875)+0.12(401259875)+ 0.22(4500040125)=$5,690. 1. For this problem, we want to write a function that gives the tax rate for any taxable amount x (in dollars). a. First, write a function M(x) that gives the federal marginal tax rate as a function of taxable income, x. Note that this will be a piecewise function. b. Sketch a graph of y=M(x). A rough sketch is fine! You may use Desmos or sketch the graph on paper. Make sure to label your axes. c. What does the ordered pair (10000,0.12) represent on the graph of y=M(x) ? d. What is M(100,000) ? What does that value represent? MATH 115 Cilli-Turner Modeling Problem #2 PIECEWISE FUNCTIONS (SECTION 3.2) STANDARD: F1 Federal and state income tax is computed within income brackets and your taxable amount (income) is separated into an amount owed in each bracket. Each of the percentages you see below is called a marginal tax rate. Each rate applies only to an amount earned that is within a particular bracket. That means that if your taxable income $45,000, you would owe 10% on the first $9,875,12% on the portion from $9,875 to $40,125 (so on a total of $30,250 ), and 22% on the portion from $40,125 to $45,000. Thus, your total tax paid would be 0.1(9875)+0.12(401259875)+ 0.22(4500040125)=$5,690. 1. For this problem, we want to write a function that gives the tax rate for any taxable amount x (in dollars). a. First, write a function M(x) that gives the federal marginal tax rate as a function of taxable income, x. Note that this will be a piecewise function. b. Sketch a graph of y=M(x). A rough sketch is fine! You may use Desmos or sketch the graph on paper. Make sure to label your axes. c. What does the ordered pair (10000,0.12) represent on the graph of y=M(x) ? d. What is M(100,000) ? What does that value represent