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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

Math 170 Functions, Data, and Models

09 Piecewise-Defined Functions Section 2.3

Comments on Lab 02.

basic concept
Basic Concept
  • A function can be defined piecewise.
tax example
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
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
Graph Example
  • Find a formula for the given graph.
formula examples
Formula Examples
  • Suppose . Graph on a suitable domain.
  • Suppose g. Is a function?
  • Suppose h. Is a function?
absolute value example
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?