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Math 170 Functions, Data, and Models

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

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  1. Math 170 Functions, Data, and Models 09 Piecewise-Defined Functions Section 2.3 Comments on Lab 02.

  2. Basic Concept • A function can be defined piecewise.

  3. 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?

  4. 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 .

  5. Graph Example • Find a formula for the given graph.

  6. Formula Examples • Suppose . Graph on a suitable domain. • Suppose g. Is a function? • Suppose h. Is a function?

  7. 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?

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