Math 170 Functions, Data, and Models

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Math 170 Functions, Data, and Models. 09 Piecewise-Defined Functions Section 2.3. Comments on Lab 02. Basic Concept. A function can be defined piecewise. Tax Example. The U.S. Income Tax rates for the first three tax brackets are 10 % on taxable income from \$0 to \$ 8,700,

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### Math 170 Functions, Data, and Models

09 Piecewise-Defined Functions Section 2.3

Basic Concept
• A function can be defined piecewise.
Tax Example
• The U.S. Income Tax rates for the first three tax brackets are
• 10% on taxable income from \$0 to \$8,700,
• 15% on taxable income over \$8,700 to \$35,350
• 25% on taxable income over \$35,350 to \$85,650
• Find the income tax paid on taxable incomes of \$1,000, \$10,000, and \$50,000.
• Draw a graph of income tax paid as a function of taxable income.
• Find a formula for income tax paid as a function of taxable income.
• How can it be that 47% of adult pay no federal income tax?
Paint Example
• Consider , where is the number of gallon cans of paint to be bought to cover a surface of square meters. Suppose 1 gallon of paint covers 9 square meters.
• What is , , and
• Draw a graph of on the domain .
• Find a formula for on the domain .
Graph Example
• Find a formula for the given graph.
Formula Examples
• Suppose . Graph on a suitable domain.
• Suppose g. Is a function?
• Suppose h. Is a function?
Absolute Value Example
• The absolute value of , denoted , is the distance is from the origin.
• Find , , and .
• Graph the absolute value function.
• Find a formula for the absolute value function.
• What is the domain and range of the absolute value function?