Functions, Arithmetic and Geometric Progression, Matrix
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A function describes the relationship between variables where a change in one variable causes a change in the other. The independent variable is called the domain and the dependent variable is called the range. Functions can be explicit, where the dependent variable is directly defined in terms of the independent variable, or implicit, where the variables are mixed in the relationship. Functions can also be increasing or decreasing based on whether the dependent variable increases or decreases as the independent variable increases. Other types of functions include even functions, where f(-x)=f(x), odd functions where f(-x)=-f(x), and polynomial functions defined by a polynomial equation.
Functions, Arithmetic and Geometric Progression, Matrix
- 1. Function & Types Of Function Name:-Aamir Zahoor Class :- Subject: - Roll No: - Submitted to:- http://www.slideshare.net/aamirzahoor1
- 2. Functions The term ‘functions’ refers to the relationship between the variables. When change in one variable is observed due to change in the other variable , then it is said to have functional relationship. In other words , a variable `y’ is said to be a function of another variable `x’ when to every value of `x’ there corresponds a definite value of `y’. It is written as y = f (x) Here `x’ is called ind.ependent variable and `y’ is called dependent variable http://www.slideshare.net/aamirzahoor1
- 3. Domain and Range of Function The set of values which an independent variable can assume is called the domain of the function and the set of corresponding values of y(i.e. dependent variable) is called the range of the function. Functions are helpful to understand the relation among different Input and Output variables of Business. http://www.slideshare.net/aamirzahoor1
- 4. Types of Functions Functions Functions are classified into the following categories Explicit and Implicit Functions : -A function y f(x) is said to be an explicit function of x if the value of y is directly given in terms of x. It is written as y = f(x) But if the variables y and x are mixed in the functional relationship, then the function is said to be an implicit function It is written as f(x,y) = 0 http://www.slideshare.net/aamirzahoor1
- 5. Increasing and Decreasing Functions:- A function (x) is said to be an increasing function of x if the value of y always increases as x increases. The function (x) is said to be a decreasing function of x if the value of y always decreases as the value of x increases. Normal demand functions and total cost functions are decreasing and increasing functions respectively. Even and Odd functions : -A function f(x) is said to be an even function of x if f(-x)=f(x). e.g. (x) = X2is even function. Similarly a function f(x) is said to be an odd function of x if f(-x)= -f(x).e.g. f(x) = x3is an odd function. http://www.slideshare.net/aamirzahoor1
- 6. Polynomial Functions :- A function of the form Y = f(x) = a0 + A1 x +a2x2 + …………………….… anxn where n is a positive integer and ,a1 ≠ 0 is called a polynomial function of degree n. If n=0, we have y = f(x) = a , a constant function http://www.slideshare.net/aamirzahoor1