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This module describes notation for functions.

Function notation

Functions are represented in math by parentheses. When you write f ( x ) size 12{f \( x \) } {} you indicate that the variable f size 12{f} {} is a function of—or depends on—the variable x size 12{x} {} .

For instance, suppose f ( x ) = x 2 + 3x size 12{f \( x \) =x rSup { size 8{2} } +3x} {} . This means that f is a function that takes whatever you give it, and squares it, and multiplies it by 3, and adds those two quantities.

7 10 x y a dog x-squared plus 3x Gearbox f ( 7 ) = 7 2 + 3 ( 7 ) = 70 f ( 10 ) = 10 2 + 3 ( 10 ) = 130 f ( x ) = x 2 + 3x f ( y ) = y 2 + 3y f ( dog ) = ( dog ) 2 + 3 ( dog ) ( *not in the domain )

The notation f ( 7 ) size 12{f \( 7 \) } {} means “plug the number 7 into the function f size 12{f} {} .” It does not indicate that you are multiplying f size 12{f} {} times 7. To evaluate f ( 7 ) size 12{f \( 7 \) } {} you take the function f ( x ) size 12{f \( x \) } {} and replace all occurrences of the variable x with the number 7. If this function is given a 7 it will come out with a 70.

If we write f ( y ) = y 2 + 3y size 12{f \( y \) =y rSup { size 8{2} } +3y} {} we have not specified a different function . Remember, the function is not the variables or the numbers, it is the process. f ( y ) = y 2 + 3y size 12{f \( y \) =y rSup { size 8{2} } +3y} {} also means “whatever number comes in, square it, multiply it by 3, and add those two quantities.” So it is a different way of writing the same function.

Just as many students expect all variables to be named x size 12{x} {} , many students—and an unfortunate number of parents—expect all functions to be named f size 12{f} {} . The correct rule is that—whenever possible— functions, like variables, should be named descriptively . For instance, if Alice makes $100/day, we might write:

  • Let m equal the amount of money Alice has made (measured in dollars)
  • Let t equal the amount of time Alice has worked (measured in days)
  • Then, m ( t ) = 100 t size 12{m \( t \) ="100"t} {}

This last equation should be read “ m size 12{m} {} is a function of t size 12{t} {} (or m size 12{m} {} depends on t size 12{t} {} ). Given any value of the variable t size 12{t} {} , you can multiply it by 100 to find the corresponding value of the variable m size 12{m} {} .”

Of course, this is a very simple function! While simple examples are helpful to illustrate the concept, it is important to realize that very complicated functions are also used to model real world relationships. For instance, in Einstein’s Special Theory of Relativity, if an object is going very fast, its mass is multiplied by 1 1 v 2 9 10 16 size 12{ { {1} over { sqrt {1 - { {v rSup { size 8{2} } } over {9 cdot "10" rSup { size 8{"16"} } } } } } } } {} . While this can look extremely intimidating, it is just another function. The speed v size 12{v} {} is the independent variable, and the mass m size 12{m} {} is dependent. Given any speed v size 12{v} {} you can determine how much the mass m size 12{m} {} is multiplied by.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Advanced algebra ii: conceptual explanations. OpenStax CNX. May 04, 2010 Download for free at http://cnx.org/content/col10624/1.15
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