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From the point of construction of the graph of y=f(|x|), we need to modify the graph of y=f(x) as :

1 : remove left half of the graph

2 : take the mirror image of right half of the graph in y-axis

This completes the construction for y=f(|x|).

Problem : Draw graph of y = sin | x | .

Solution : First we draw graph of sinx. In order to obtain the graph of y=sin|x|, we remove left half of the graph and take the mirror image of right half of the graph of in y-axis.

Modulus operator applied to sine function

Modulus operator applied to the argument of sine function.

Problem : Draw graph of y = e | x + 1 | .

Solution : We first draw graph of y = e x . Then, we shift the graph left by 1 unit to obtain the graph of e x + 1 . At x = 0, y = e 0 + 1 = e . In order to obtain the graph of y = e | x + 1 | , we remove left part of the graph and take the mirror image of right half of the graph of y = e x + 1 in y-axis.

Modulus operator applied to exponential function

Modulus operator applied to the argument of exponential function.

In order to obtain the graph of y = e | x + 1 | , we remove left part of the graph and take the mirror image of right half of the graph of y = e x + 1 in y-axis.

Problem : Draw graph of y = x 2 2 | x | 3

Solution : The given expression f x = x 2 2 | x | 3 is obtained by taking modulus of the independent variable of the corresponding quadratic polynomial in x as given here, f x = x 2 - 2 x - 3 . Hence, we first draw f x = x 2 - 2 x - 3 . The corresponding quadratic equation f x = x 2 - 2 x - 3 = 0 has real roots -1 and 3. The co-efficient of “ x 2 ” is positive. Hence, its plot is a parabola which opens upward and intersects x-axis at x=-1 and x=3.

In order to draw the graph of f x = | x | 2 2 | x | 3 = x 2 2 | x | 3 , we remove left half of the graph and take the mirror image of right half of the core graph of quadratic function in y-axis.

Modulus operator applied to quadratic function

Modulus operator applied to the quadratic function.

Problem : Draw graph of function defined as :

y = 1 | x | + 1

Solution : It is clear that we can obtain given function by applying modulus operator to the independent variable of function given here :

y = 1 x + 1

This function, in tern, can be obtained by applying shifting modification to the argument of the function given as :

y = 1 x

We, therefore, first draw f x = 1 / x . Then we draw g x = f x + 1 = 1 / x + 1 by shifting the graph left by 1 unit. Finally, we draw h x = g | x | = 1 / | x | + 1 by removing left half of the graph and taking mirror image of right half of the graph in y-axis. .

Modulus operator applied to rational function

Modulus operator applied to the argument of rational function.

Modulus function applied to the function

The form of transformation is depicted as :

y = f x y = | f x |

It can be seen that modulus operator here modifies the value of the function itself. In other words, it is like changing output of the function in accordance with nature of modulus function. The output of the function is now either zero or positive number. This has the implication that part of the graph y=f(x) corresponding to negative function values is not present in the graph of y=|f(x)|. Rather, negative function value of f(x) is converted to positive function value. This change in the sign of function takes place without changing magnitude of the value. It implies that we can obtain function values, which correspond to negative function value in y=f(x) by taking image of negative function values across x-axis. This is image in x-axis.

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
Maciej
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 ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
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
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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, Functions. OpenStax CNX. Sep 23, 2008 Download for free at http://cnx.org/content/col10464/1.64
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