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 f(x)=sin x  means the sine of the angle whose radian measure is x

properties

6. Exponential Function

7. Logarithmic Function

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

Ex Classify the following functions as one of the types of functions !

Answer

Transformations of Funstions

Stretching & Reflecting

Combinations of Functions

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

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

Composite function

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

Ex if Find each function and its domain!

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 !

One to One Function

Is the function one to one?

Graph!

Inverse Function

Cancellation Law