Functions
Download as PPT, PDF1 like358 views
The document introduces the concept of functions and their graphical representations, detailing the relationship between input (domain) and output (co-domain). It discusses various applications of functions in fields like anthropology, civil engineering, and microbiology, and explains important properties such as the vertical line test. Additionally, it covers different types of functions, including polynomial and variations like direct and inverse variation.
Functions
- 1. Chapter One : Functions, Graphs and Graphers.
- 2. The idea of a function.
- 3. The distance, in miles, is 1/5 of the time, in seconds. 15 seconds --> 3 miles
- 4. x 15 3 (15,3) 3 15 10 2 (10,2) 2 10 5 1 (5.1) 1 5 1 1/5 (1,1/5) 1/5 1 0 0 (0,0) 0 0 Correspondence Ordered pairs (x,y) y
- 6. y = (1/5)x Distance is a function of time.
- 7. A function is a correspondence between a first set, called domain , and a second set, called the co-domain , and only the elements which have a pre-image in the domain, make up the range.
- 8. Notation – inputs (members of the domain) are values of x outputs (members of the range) are values of y
- 9. function f input x corresponding output f (x)
- 10. f (x) does not mean f*x
- 11. ?
- 12. Vertical Line Test If it is possible for a vertical line to cross a graph more than once, then the graph is not a graph of a function.
- 14. Finding the domain – The input should give real output
- 15. f (x)=
- 17. Speed of Sound
- 20. t=temperature in Fahrenheit; S=speed of sound in feet/sec boeing.com/commercial/industry_info.html
- 21. 1544.955 500 1464.967 400 1380.511 300 1290.197 200 1193.292 100 1087.700 0 970.737 -100 837.599 -200 678.823 -300 469.099 -400 Y X
- 22. Temp Speed
- 23. Temp Speed
- 24. Temp Speed
- 25. Temp
- 26. Temp
- 29. Anthropology
- 30. humerus
- 31. 131.98 22 151.23 29 142.98 26 F(x) X
- 32. Humerus Height
- 33. Height
- 34. y = 2.5x + 71.48
- 35. Height Humerus
- 41. For a run of hundred feet, a rise of twenty feet is permitted.
- 42. x = run f(x) = rise
- 45. Meteorology
- 47. Temp in F Month
- 48. polynomial function 0.2607392 x 2 + 3.620379 x + 72.090909
- 52. 400 ft 120 t d Express d as a function of t
- 54. Population
- 55. N 0 is the starting population N is the population after a certain time, t , has elapsed, r is the rate of natural increase ( birth rate - death rate ) and e is the constant 2.71828...
- 58. Microbiologists
- 59. 2048 11 1024 10 512 9 256 8 128 7 64 6 32 5 16 4 8 3 4 2 2 1 1 0 Cells Time
- 60. Time (sec) Cells
- 62. A cardioid is a curve that can be produced as the path (or locus) of a point on the circumference of a circle as that circle rolls around another fixed circle with the same radius. wiki
- 64. Cos = red Exp = black Mathworld.wolfram.com
- 65. Hoffman-Singleton graph Mathworld.wolfram.com
- 66. Variation
- 67. Direct variation
Editor's Notes
- #2: Chapter One : Functions, Graphs and Graphers.