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
Definition of a Function Now we need to move into the second topic of this chapter.  Before we do that however we must look a quick definition taken care of.

* 2^(1/2)*4^(1/8)*8^(1/16)*16^(1/32) =


Conditional probability - Rules of Probability This is the probability associated with combinations of events but given that some prior result has already been achieved with o

Write following in terms of simpler logarithms.  (a) log 3 (9 x 4    / √y) Solution log 3 (9 x 4 / √y) =log ­ 3 9x 4 -  log  y (1/2) =log ­ 3 9 + log ­ 3 x 4

Discuss demanding total market demand verus gaing market share

Can you please explain what Quadratic functions are?

R is called as a transitive relation if (a, b) € R, (b, c) € R → (a, c) € R In other terms if a belongs to b, b belongs to c, then a belongs to c.         Transitivity be uns