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Section 2.3 Piecewise Defined Functions

Section 2.3 Piecewise Defined Functions. Piecewise Defined Functions- when a function uses different formulas on different parts of its domain. Piecewise Defined Functions- when a function uses different formulas on different parts of its domain. An example:.

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Section 2.3 Piecewise Defined Functions

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  1. Section 2.3 Piecewise Defined Functions

  2. Piecewise Defined Functions- when a function uses different formulas on different parts of its domain. Page 73

  3. Piecewise Defined Functions- when a function uses different formulas on different parts of its domain. An example: Page 73

  4. Here is a graph of this piecewise function: Page 73

  5. Piecewise Defined Functions- Another example: g(x) = x + 1 for x ≤ 2 and g(x) = 1 for x > 2 Let's graph this function: Page 73 Example 1

  6. g(x) = x + 1 for x ≤ 2 and g(x) = 1 for x > 2 Page 73

  7. A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. a. Use bracket notation to write a formula for the cost, C, of a call as a function of its length t in minutes. b. Graph the function. c. State the domain and range of the function. Page 2 Example #2

  8. A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. a. Use bracket notation to write a formula for the cost, C, of a call as a function of its length t in minutes. Page 74

  9. You can simplify this expression to get: Page 74

  10. But you lose the real meaning by doing so. Page 74

  11. A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. b. Graph the function. Page 74

  12. A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. b. Graph the function. Page 74

  13. A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function. Page 74

  14. A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function. Domain: t > 0 (call lengths ≤ 0 are silly) Page 74

  15. A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. c. State the domain and range of the function. Domain: t > 0 (call lengths ≤ 0 are silly) Range? Page 74

  16. A long-distance calling plan charges 99 cents for any call up to 20 minutes in length and 7 cents for each additional minute or part of a minute. Range? We can see that the range is: C ≥ 99 Page 74

  17. The Absolute Value Function Page 76

  18. The Absolute Value Function (defined piecewise): Page 76

  19. Some examples: Page 76

  20. Some examples: Page 76

  21. Some examples: Page 76

  22. Some examples: Page 76

  23. Let's form a table and then graph the absolute value function: Page 76

  24. Page 76

  25. Page 76

  26. This completes Section 2.3 Page

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