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Chapter 2: Functions and Graphs

Chapter 2: Functions and Graphs. PART 2. Increasing & Decreasing Function. Many type of Function. 1. LINEAR FUNCTION. 2. Polynomial. EXAMPLE. 3. Power Function. ii. a=1/n, n is a positive integer. iii. a=-1. 4. Rational Function. 5. Algebraic Function. 6. Trigonometri Function.

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Chapter 2: Functions and Graphs

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  1. Chapter 2: Functions and Graphs PART 2

  2. Increasing & Decreasing Function

  3. Many type of Function 1. LINEAR FUNCTION

  4. 2. Polynomial

  5. EXAMPLE

  6. 3. Power Function

  7. ii. a=1/n, n is a positive integer

  8. iii. a=-1

  9. 4. Rational Function

  10. 5. Algebraic Function

  11. 6. Trigonometri Function f(x)=sin x  means the sine of the angle whose radian measure is x

  12. properties

  13. 6. Exponential Function

  14. 7. Logarithmic Function

  15. 8. Trancendental Function •  are functions that are not algebraic •  includes : trigonometric, inverse trigonometric, exponential, logarithmic function

  16. Ex • Classify the following functions as one of the types of functions !

  17. Answer

  18. Transformations of Funstions

  19. Stretching & Reflecting

  20. Combinations of Functions

  21. OPERATIONs On FUNCTIONs • Given skalar real a and function f,g then the definition of the function operation is given by : • (f+g)(x)= f(x) + g(x) • (f-g)(x)=f(x) - g(x) • (af)(x) = a f(x) • (f.g)(x)= f(x)g(x) • (f/g)(x)= f(x)/g(x), g(x)≠0 Each domain function above is the intersection Df and Dg except for f /g

  22. If find the functions f+g, f-g, fg, f/g and the domain

  23. Composite function

  24. Composition Function • Compositon function from function f and g, is denoted by fg thus ; (f g)(x)=f(g(x)) • With domain function :

  25. Ex if Find each function and its domain!

  26. Given :then find :a. f + g , f - g , f .g , and f/ g b. Each the domain function !

  27. One to One Function

  28. Is the function one to one?

  29. Graph!

  30. Inverse Function

  31. Cancellation Law

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