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2. Chapter 2 Section 2 Domain and Range 2

3. If Q = f ( t ), then: (a) the domain of f is the set of input values, t, which yield an output value. (b) the range of f is the corresponding set of output values, Q. Page 69 Blue Box3

4. If there are no restrictions, domain of the function is the set of all real numbers. Page 694

5. If there are no restrictions, domain of the function is the set of all real numbers. However, if a function is used to model a real-world situation, the domain and range of the function are often restricted: Page 695

6. Is there any restriction in the domain regarding the house painting example: n = f(A) = A/250? Page 69 Example 16

7. If there any restriction in the domain regarding the house painting example: n = f(A) = A/250? A (area of house) > 0 Page 697

8. If there any restriction in the range regarding the house painting example: n = f(A) = A/250? Page 698

9. If there any restriction in the range regarding the house painting example: n = f(A) = A/250? n (# of gal. of paint) > 0 (book says n ≥ 0 (if gal. rounded to nearest whole #) Page 699

10. When a function is used to model a real situation, it may be necessary to modify the domain and range. Page 6910

11. Let's revisit our "cricket" function: Page 69 Example 211

12. Let's revisit our "cricket" function: Domain and/or range restrictions? Page 6912

13. Let's revisit our "cricket" function: Domain and/or range restrictions? In theory, none... Page 6913

14. Domain and/or range restrictions? Page14

15. Domain and/or range restrictions? if 0 ≤ R ≤ R max Page15

16. Domain and/or range restrictions? if 0 ≤ R ≤ R max, then 40 ≤ T ≤ T max Page16

17. Using a Graph to Find the Domain and Range of a Function Page 7017

18. To review: Domain = the set of input values on the horizontal axis which give rise to a point on the graph; Range = corresponding set of output values on the vertical axis. Page 7018

19. A sunflower plant is measured every day t, for t ≥ 0. The height, h ( t ) centimeters, of the plant can be modeled by using the logistic function: (a) Using a graphing calculator or computer, graph the height over 80 days. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Page 70 Example 319

20. (a) Using a graphing calculator or computer, graph the height over 80 days. Page 7020

21. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Page 7021

22. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Domain: t ≥ 0 Page 7022

23. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Domain: t ≥ 0 BUT... Page 7023

24. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Domain: t ≥ 0 Since sunflower will die... ? Page 7024

25. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Domain: t ≥ 0 Since sunflower will die 0 ≤ t ≤ T, where T is the day that the sunflower dies. Page 7025

26. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? Page 7126

27. A reminder of what the graph looks like. Page 7027

28. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? What is the minimum value of h? Page 7128

29. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? What is the minimum value of h? When t = 0, h = 10.4 cm. Page 7129

30. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? What is the minimum value of h? When t = 0, h = 10.4 cm. Maximum value of h? Page 7130

31. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? What is the minimum value of h? When t = 0, h = 10.4 cm. Maximum value of h? As t increases, h(t) approaches 260 cm. Page 7131

32. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? 10.4 ≤ h(t) ≤ 260 Page 7132

33. Using a Formula to Find the Domain and Range of a Function Page 7133

34. State the domain and range of g, where: g(x) = 1 / x Page 71 Example 434

35. State the domain and range of g, where: g(x) = 1 / x Domain: all real numbers, except that x ≠ 0 Page 7135

36. State the domain and range of g, where: g(x) = 1 / x Domain: all real numbers, except that x ≠ 0 Range = ? Page 7136

37. State the domain and range of g, where: g(x) = 1 / x Domain: all real numbers, except that x ≠ 0 Range = ? Range is all real numbers except 0 (since 1/x can't = 0 ). Page 7137

38. Page38

39. Find the domain of: Page 71 Example 539

40. Find the domain of: What can't x = ? Page 7140

41. Find the domain of: If we eliminate complex numbers, domain = ? Page 7141

42. Find the domain of: Domain: x > 4 Page 7142

43. Find the range of: Page 7143

44. Find the range of: Since domain: x > 4, range = ? Page 7144

45. Find the range of: Since domain: x > 4, range: f(x) > 0 Page 7145

46. End of Section 2.2 46