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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

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Math 1508 (lecture) readings in precalculus. OpenStax CNX. Aug 24, 2011 Download for free at http://cnx.org/content/col11354/1.1
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