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

24. Composite function

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

26. Ex if
Find each function and its domain!

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

28. One to One Function

29. Is the function one to one?

30. Graph!

31. Inverse Function

32. Cancellation Law