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Comprehensive Guide to Different Types of Functions and Operations

This comprehensive guide covers various types of functions like Linear, Polynomial, Power, Rational, Algebraic, Trigonometric, Exponential, Logarithmic, and Transcendental functions. It also includes operations on functions such as addition, subtraction, scalar multiplication, multiplication, division, and composition. Learn about transformations, stretching, reflecting, combinations of functions, one-to-one functions, inverse functions, and the cancellation law.

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Comprehensive Guide to Different Types of Functions and Operations

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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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