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 fg 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