Linear Functions and Change Functions & Function notation

2. Chapter 1 Section 1 Linear Functions and Change Functions & Function notation

3. A function is a rule which takes certain numbers as inputs and assigns to each input number exactly oneoutput number. The output is a function of the input. The inputs and outputs are also called variables. Page 2

4. Page N/A

5. “Oecanthus Fultoni” Page N/A

6. “The Snowy Tree Cricket” Page N/A

7. “Nature’s Thermometer" Page N/A

8. By counting the number of times a snowy tree cricket chirps in 15 seconds... Page 2 (Example 1)

9. By counting the number of times a snowy tree cricket chirps in 15 seconds & adding 40... Page 2

10. By counting the number of times a snowy tree cricket chirps in 15 seconds & adding 40... We can estimate the temperature (in degrees Fahrenheit)!!! Page 2

11. For instance, if we count 20 chirps in 15 seconds, then a good estimate of the temperature is? Page 2

12. For instance, if we count 20 chirps in 15 seconds, then a good estimate of the temperature is? 20 + 40 = 60°F!!!! Page 2

13. Page 3

14. T R Page 3

15. Page 3

16. Page 3

17. By doing more substitutions into the formula, we can create: Page 3

18. Page 3

19. From this table, we can create: Page 3

20. Page 3

21. When we use a function to describe an actual situation, the function is referred to as a mathematical model. is a mathematical model of the relationship between the temperature and the cricket's chirp rate. Page 3

22. What is the chirp rate when the temperature is 40 degrees? Page 4

23. Page 4

24. Page 4

25. Page 4

26. Page 4

27. Page 4

28. Page 4

29. What if the temperature is 30 degrees? What is R? Page 4

30. Page 4

31. Page 4

32. What is the moral here? Page 4

33. Whether the model's predictions are accurate for chirp rates down to zero and temperatures as low as 40°F is a question that mathematics alone cannot answer; an understanding of the biology of crickets is needed. However, we can safely say that the model does not apply for temperatures below 40°F, because the chirp rate would then be negative. For the range of chirp rates and temperatures in Table 1.1, the model is remarkably accurate. Page 4

34. Page 4

35. Is T a function of R, or vice-versa? Page 4

36. T is a function of R. Page 4

37. Will making the cricket chirp faster (or slower) result in a temperature change upward (or downward)?!? Page 4

38. Will making the cricket chirp faster (or slower) result in a temperature change upward (or downward)?!? No Page 4

39. Saying that the temperature (T) depends on the chirp rate (R) means: Knowing the chirp rate (R) is sufficient to tell us the temperature (T). Page 4

40. Saying that the temperature (T) depends on the chirp rate (R) means: Knowing the chirp rate (R) is sufficient to tell us the temperature (T). Again, a change in the chirp rate (R) doesn't cause a change in the temperature (T). Page 4

41. A function is a rule which takes certain numbers as inputs and assigns to each input number exactly oneoutput number. The output is a function of the input. The inputs and outputs are also called variables. Page 2

42. Function Notation Q is a function of quantity, t Or: Q is a function of t We abbreviate: Q = “f of t” or Q = f(t). Page 4

43. Q = f(t) This means: applying the rule f to the input value, t, gives the output value, f(t). Here: Q = dependent variable (unknown, depends on t) t = independent variable (known) Page 4

44. Q = f(t). In other words: Output = f(Input) Or: Dependent = f(Independent) Page 4

45. The number of gallons of paint needed to paint a house depends on the size of the house. A gallon of paint typically covers 250 square feet. Thus, the number of gallons of paint, n, is a function of the area to be painted, A ft2. We write n = f(A). (a)  Find a formula for f. (b)  Explain in words what the statement f(10,000) = 40 tells us about painting houses. Page 4 (Example 2)

46. The number of gallons of paint needed to paint a house depends on the size of the house. A gallon of paint typically covers 250 square feet. Thus, the number of gallons of paint, n, is a function of the area to be painted, A ft2. We write n = f(A). (a)  Find a formula for f. If n = 1, A = ? ft2 Page 4

47. The number of gallons of paint needed to paint a house depends on the size of the house. A gallon of paint typically covers 250 square feet. Thus, the number of gallons of paint, n, is a function of the area to be painted, A ft2. We write n = f(A). (a)  Find a formula for f. If n = 1, A = 250 ft2 Page 4

48. The number of gallons of paint needed to paint a house depends on the size of the house. A gallon of paint typically covers 250 square feet. Thus, the number of gallons of paint, n, is a function of the area to be painted, A ft2. We write n = f(A). (a)  Find a formula for f. If n = 2, A = ? ft2 Page 4

49. The number of gallons of paint needed to paint a house depends on the size of the house. A gallon of paint typically covers 250 square feet. Thus, the number of gallons of paint, n, is a function of the area to be painted, A ft2. We write n = f(A). (a)  Find a formula for f. If n = 2, A = 500 ft2 Page 4

50. The number of gallons of paint needed to paint a house depends on the size of the house. A gallon of paint typically covers 250 square feet. Thus, the number of gallons of paint, n, is a function of the area to be painted, A ft2. We write n = f(A). (a)  Find a formula for f. If n = 3, A = ? ft2 Page 4