<< Chapter < Page Chapter >> Page >

A function like y=f(x) has different elements. We can apply modulus operator to these elements of the function. There are following different possibilities :

1 : y = f | x |

2 : y = | f x |

3 : | y | = f x

4 : x = | f y |

Plotting concept

The most important point about plotting is to understand that application of modifying operator has different interpretation whether it is applied to independent variable “x” or function definition in x like “f(x)” or it is applied to dependent variable “y” or function definition like “f(y)”. There is a difference in the approach to interpretation.

Clearly, modulus operations have different implications for the graph of f(x). In general, every function can be interpreted to be an operator which operates on its argument, which in itself can be variable like “x”, expression like “ x 2 + 2 ” or other functions. This role is more visible for functions like modulus, greatest integer, fraction part and least integer function. For this reason, these functions are represented by symbolic notations like | |, [], {} and () as operators.

When operator is applied to independent variable or function definition, we evaluate operation of the operator on independent variable or function value. Here, interpretation is based on “evaluation” of the expression (independent variable or function definition) and application of operator thereafter. This applies to the transformations enumerated at (i) and (ii) above. Consider for example,

y = | f x |

The function of value at any value x=x is first evaluated. Then, modulus of value is calculated. Finally, it is assigned to y as its value.

This basis of interpretation changes when we apply operator to dependent variable “y” or function definition in “y”. Now the basis of interpretation is that of “assigning” a value to a function and then interpreting the assignment. Such is the case with transformations enumerated at (iii) and (iv) above. Consider for example,

| y | = f x

In this case, value of function evaluated at x=x is assigned to modulus function. We interpret equality of the modulus function [y] to a value in accordance with modulus definition. In this case, we know that :

| y | = a ; a > 0 y = ± a

| y | = a ; a = 0 y = 0

| y | = a ; a < 0 Modulus can not be equated to negative value. No solution

From the point of view of construction of plot, for a single positive value of f(x), say f(x)=4, we have two values of dependent variable i.e. -4 or 4. This needs to be considered while plotting |y|=f(x). In the plot, values of y are plotted against values of x. In this particular instant, there are two points (4,4) and (4,-4) on the graph corresponding to one value of independent variable (4).

Modulus function applied to the independent variable

The form of transformation is depicted as :

y = f x y = f | x |

It can be seen that modulus operator here modifies independent varaible of the function. In other words, it is like changing input to the function in accordance with nature of modulus function. The input to the function is now either zero or positive number. This has the implication that part of the graph y=f(x) corresponding to negative value of x is not present in the graph of y=f(|x|). Rather, negative value of x is passed as positive value to the function. This means that negative value of independent variable x yields function value which is equal to function value obtained for corresponding positive x whose magnitude is same as that corresponding negative x. It implies that we can obtain function value for negative x by taking image of positive x across y-axis. This is image in y-axis.

Questions & Answers

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
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.
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
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Berger describes sociologists as concerned with
Mueller Reply
What is power set
Satyabrata Reply
Period of sin^6 3x+ cos^6 3x
Sneha Reply
Period of sin^6 3x+ cos^6 3x
Sneha Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Functions. OpenStax CNX. Sep 23, 2008 Download for free at http://cnx.org/content/col10464/1.64
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Functions' conversation and receive update notifications?