Definition of a function, Mathematics

Assignment Help:

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.


Related Discussions:- Definition of a function

Elliptic paraboloid - three dimensional spaces, Elliptic Paraboloid Th...

Elliptic Paraboloid The equation which is given here is the equation of an elliptic paraboloid. x 2 /a 2 + y 2 /b 2 = z/c Like with cylinders this has a cross section

Mathematic Modeling, Ask question I have 2 problems I need them after 7 hou...

Ask question I have 2 problems I need them after 7 hours

Subspace of r containing n, Give an example of each of the following given ...

Give an example of each of the following given below . You do not require to give any justi cation. (a) A nonempty, bounded subset of Q with no in mum in Q. (b) A subspace of

Complement of a set, Need solution For the universal set T = {1, 2, 3, 4...

Need solution For the universal set T = {1, 2, 3, 4, 5} and its subset A ={2, 3} and B ={5, } Find i) A 1 ii) (A 1 ) 1 iii) (B 1 ) 1

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that each word contain 2vowles and 3consonant

Ratios, the ratio of boys to girls in the sixth grade is 2:3 if there are ...

the ratio of boys to girls in the sixth grade is 2:3 if there are 24 boys, how many are girls?

Difference between absolute and relative in the definition, Difference betw...

Difference between absolute and relative in the definition Now, let's talk a little bit regarding the subtle difference among the absolute & relative in the definition above.

E is irrational, If e were rational, then e = n/m for some positive integer...

If e were rational, then e = n/m for some positive integers m, n. So then 1/e = m/n. But the series expansion for 1/e is 1/e = 1 - 1/1! + 1/2! - 1/3! + ... Call the first n v

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd