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

Practice, #question.Mai is 3 years ypunger than twice the age of her brothe...

#question.Mai is 3 years ypunger than twice the age of her brother .If b represents .

Example of addition of signed numbers, Example of addition of Signed Number...

Example of addition of Signed Numbers: Example: (-2) + 3 + 4 = 0 - 2 + 3 + 4 Solution: Thus: (-2) + 3 + 4 = 5  Example: 10 + (-5) + 8 + (-7)

Projects, maths projects for class 11

maths projects for class 11

Modelling the maximum volume, what are the dimensions of the box that can b...

what are the dimensions of the box that can be made if squares of x cm by x cm is cut off from 20cm by 20cm square paper

Sin3? = cos2? find the most general values of ?, sin3θ = cos2θ find the mos...

sin3θ = cos2θ find the most general values of θ satisfying the equatios? sinax + cosbx = 0 solve ? Solution)  sin (3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x) = 2sin(x)cos(

Detremine the surface area to the nearest inch, If a tabletop has a diamete...

If a tabletop has a diameter of 42 in, Detremine the surface area to the nearest inch? (π = 3.14) a. 1,384 in 2 b. 1,319 in 2 c. 1,385 in 2 d. 5,539 in 2 c. Th

The coordinate axes, Trace the curve y 2 = (x + 2) 2 (x - 6). Clearly sta...

Trace the curve y 2 = (x + 2) 2 (x - 6). Clearly state all the properties you have used for tracing it(e.g., symmetry about the axes, symmetry about the origin, points of interse

Absolute value of a number, At times we consider only the magnitude o...

At times we consider only the magnitude of the number without attaching much importance to its direction. Under these circumstances the sign attached with the num

Substitution rule for definite integrals, Substitution Rule for Definite In...

Substitution Rule for Definite Integrals Now we need to go back and revisit the substitution rule as it also applies to definite integrals.  At some level there actually isn't

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