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

Prime factors, I need help with prime factors.

I need help with prime factors.

Find their present ages of son and father, When the son will be as old as t...

When the son will be as old as the father today their ages will add up to 126 years. When the father was old as the son is today, their ages add upto 38 years.  Find their present

What was the planes average speed, A ?ight from Pittsburgh to Los Angeles t...

A ?ight from Pittsburgh to Los Angeles took 5 hours and covered 3,060 miles. What was the plane's average speed? Find out the rate at that Susan is traveling through dividing h

Conditional probability - rules of probability, Conditional probability - R...

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

Evaluate inverse tangents , Evaluate following limits. Solution ...

Evaluate following limits. Solution Here the first two parts are actually just the basic limits including inverse tangents and can easily be found by verifying the fol

Find solution manual, i need solution manual of "calculus and analytic geom...

i need solution manual of "calculus and analytic geometry thomas 6th edition book "

Find out primes of each denominator, Find out primes of each denominator: ...

Find out primes of each denominator: Add 1/15 and 7/10 Solution: Step 1:             Find out primes of each denominator. 15 = 5 x 3 10 = 5 x 2 Step 2:

Algebra 1, how do you factor a trinomial into a binomial ?

how do you factor a trinomial into a binomial ?

Convex rectilinear figure, the sum of the interior angles of a convex recti...

the sum of the interior angles of a convex rectilinear figure is equal to sum of the exterior angles. then the number of sides is

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