Definition of a function, Mathematics

A function is a relation for which each of the value from the set the first components of the ordered pairs is related with exactly one value from the set of second components of the ordered pair.

Let's see if we can make out just what it means.  Let's take a look at the given example that will expectantly help us figure all this out.

Example:  The following relation is a function.

{(-1, 0)  (0, -3) ( 2, -3)  (3, 0)  ( 4, 5)}

Solution

From these ordered pairs we contain the following sets of first components (that means. the first number through each ordered pair) and second components (that means the second number through each ordered pair).

1st components : {-1, 0, 2, 3, 4}                      2nd   components : {0, -3, 0, 5}

 For the set of second components observed that the "-3" occurred in two ordered pairs however we only listed it once.

In order to see why this relation is a function just picks any value from the set of first components. After that, go back up to the relation and determine every ordered pair wherein this number is the first component & list all the second components from those ordered pairs. The list of second components will contain exactly one value.

For instance let's select 2 from the set of first components.  From the relation we see that there is accurately one ordered pair along with 2 as a first component, ( 2, -3) .  Thus the list of second components (that means the list of values from the set of second components) related with 2 is exactly one number, -3.

Notice that we don't care that -3 is the second component of second ordered par in the relation. That is completely acceptable.  We just don't desire there to be any more than one ordered pair along with 2 as a first component.

We looked at single value through the set of first components for our fast example here but the result will be the similar for all the other choices.  Regardless of the option of first components there will be accurately one second component related with it.

Thus this relation is a function.

In order to actually get a feel for what the definition of a function is telling us we have to probably also check out an instance of a relation that is not a function.

Posted Date: 4/6/2013 6:17:33 AM | Location : United States







Related Discussions:- Definition of a function, Assignment Help, Ask Question on Definition of a function, Get Answer, Expert's Help, Definition of a function Discussions

Write discussion on Definition of a function
Your posts are moderated
Related Questions
write and solve a problem of multiplacation that uses: estimate explaning numbers picturs and another operation?

what is 24 diveded by 3

the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?

Solving Trig Equations : Here we will discuss on solving trig equations. It is something which you will be asked to do on a fairly regular basis in my class. Let's just see the

If a single person makes $25,00 a year, how much federal income tax will he or she have to pay ?And they are gining me a chart that says $0 to $27,050 is 15% of taxes .

A telephoned dialled number 0 to 9.if 0 is dialled first the caller is connected to the international exchange system.find the number of local calls that can be rung if a local num

(-85) from (-21) and explain me

Why -2=-x , is x=2

The line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle. solution) well you could first find the ra

Prove that the parallelogram circumscribing a circle is rhombus. Ans   Given : ABCD is a parallelogram circumscribing a circle. To prove : - ABCD is a rhombus or AB