<< 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

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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?

Ask