Functions , Mathematics

For the layman, a "function" indicates a relationship among objects. A function provides a model to describe a system. Economists refer to demand functions which refer to the sales volume of an item as a function of the item's price. Similarily, economists refer to supply function which considers production volume of an item as a function of the prevailing/projected price of the item.

A function expresses the relationship of one variable or a group of variables (called the Domain) with another variable (called the Range) by associating every member in the domain with a unique member in the range. 

Suppose X represents the "price of a good" and Y the "demand". We may postulate that Y is related to X in the sense that if we fix the price of the good, then we will be able to determine the demand. We say that Y is a function of X since we are able to compute a unique value of Y for a given value of X. We may represent the relationship as y = f(x), where f represents the relationship. It is important to note that it may be the case, though it is not necessary, that the relationship is a causal one, that is, X is the cause and Y is the effect. When the relationship is causal, we may regard X as the independent variable and Y as the dependent variable.

Thus,

y = f(x) = 2 - 3x,

y = g(x) = 2x2 - x + 100

are examples of functions. But

                   y2 = x

is not a function of X since the rule that a given value of X should yield a unique value of Y is violated. (Verify for X = 4.)

Functions can be expressed algebraically (as in y = 2x - 3) or graphically or in a tabular form.

Example 

Suppose we play a game involving the toss of two fair coins. And for every Head that turns up, you win Re.1 and for every Tail that turns up, you lose Re.1

Let D = {TT, HT, HH} and R = {-2, 0, 2}

Then the game may be represented by the function

R = f(D)

where f(TT) = -2, f(HT) = 0 and f(HH) = 2

Posted Date: 9/13/2012 5:48:07 AM | Location : United States







Related Discussions:- Functions , Assignment Help, Ask Question on Functions , Get Answer, Expert's Help, Functions Discussions

Write discussion on Functions
Your posts are moderated
Related Questions
Properties of the Indefinite Integral 1.  ∫ k f ( x ) dx = k ∫ f ( x ) dx where k refer for any number.  Thus, we can factor multiplicative constants out of indefinite integral

E1) I have a three-year-old friend. He has a lot of toy cars to play with. Playing with him once, I divided the cars into two sets. One set was more spread out and had 14 cars in i

How to creates Factor by Substitution ? Can you factor this polynomial? x 2 + 3x + 2 (For this tutorial, I'm going to assume that you know how to do some basic factorin

zeroes of polynomial 2x2-3x-2


How do you find the perimeter of an irregular shape using Pythagorean theorem?

how do you solve quadratic equations by factoring?

Prove that if x is a real number then [2x] = [x] + [x + ½ ] Ans: Let us consider x be any real number. It comprises two parts: integer and fraction. With no loss of

For the layman, a "function" indicates a relationship among objects. A function provides a model to describe a system. Economists refer to deman

Explain what are the Rules for solving linear in-equations?