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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 :

(i) take the mirror image of lower half of the graph in x-axis

(ii) remove lower half of the graph

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

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

Solution : We first draw the graph of y = cos x . Then, we take the mirror image of lower half of the graph in x-axis and remove lower half of the graph to complete the construction of graph of y = | cos x |

Modulus operator applied to cosine function

Modulus operator applied to cosine function.

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

Solution : We first draw graph y = x 2 2 x 3 . The roots of corresponding quadratic equation are -1 and 3. After plotting graph of quadratic function, we take the mirror image of lower half of the graph in x-axis and remove lower half of the graph to complete the construction of graph of y = | x 2 2 x 3 |

Modulus operator applied to quadratic function

Modulus operator applied to quadratic function.

Problem : Draw graph of y = | log 10 x | .

Solution : We first draw graph y = log 10 x . Then, we take the mirror image of lower half of the graph in x-axis and remove lower half of the graph to complete the construction of graph of y = | log 10 x | .

Modulus operator applied to logarithmic function

Modulus operator applied to logarithmic function.

Modulus function applied to dependent variable

The form of transformation is depicted as :

y = f x | y | = f x

As discussed in the beginning of module, value of function is first calculated for a given value of x. The value so evaluated is assigned to the modulus function |y|. We interpret assignment to |y| in accordance with the interpretation of equality of the modulus function to a value. In this case, we know that :

| y | = f x ; f x > 0 y = ± f x

| y | = f x ; f x = 0 y = 0

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

Clearly, we need to neglect all negative values of f(x). For every positive value of f(x), there are two values of dependent expressions -f(x) and f(x). It means that we need to take image of upper part of the graph across x-axis. This is image in x-axis.

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 lower half of the graph

2 : take the mirror image of upper half of the graph in x-axis

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

Problem : Draw graph of | y | = x 1 x 3 .

Solution : We first draw the graph of quadratic function given by y = x 1 x 3 . Then, we remove lower half of the graph and take mirror image of upper half of the graph in x-axis to complete the construction of graph of | y | = x 1 x 3 .

Modulus operator applied to dependent variable

Modulus operator applied to dependent variable.

Problem : Draw graph of | y | = tan - 1 x .

Solution : We first draw the graph of function given by y = tan - 1 x . Then, we remove lower half of the graph and take mirror image of upper half of the graph in x-axis to complete the construction of graph of y = tan - 1 x .

Modulus operator applied to dependent variable

Modulus operator applied to dependent variable.

Modulus function applied to inverse function

The form of transformation is depicted as :

Questions & Answers

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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
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
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
Good
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

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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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