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Domain and Range Report-٣

The document explains the concepts of domain and range in mathematics, defining the domain as the set of all possible input values and the range as the set of all possible output values. It discusses methods for determining domain and range, including identifying undefined values and analyzing function behavior, and highlights their applications in engineering, physics, and computer science. Understanding these concepts is essential for solving real-world problems involving input-output relationships.

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5 views2 pages

Domain and Range Report-٣

The document explains the concepts of domain and range in mathematics, defining the domain as the set of all possible input values and the range as the set of all possible output values. It discusses methods for determining domain and range, including identifying undefined values and analyzing function behavior, and highlights their applications in engineering, physics, and computer science. Understanding these concepts is essential for solving real-world problems involving input-output relationships.

Uploaded by

hhnnnhh54
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Domain and Range

Introduction

In mathematics, the concepts of domain and range play a crucial role in understanding
functions.
The domain refers to the set of all possible input values (independent variable), while the
range represents the set of all possible output values (dependent variable).
These concepts are fundamental in various fields, including engineering, physics, and
computer science.
This report will explore the definitions, methods to determine domain and range, and their
applications.

Definition of Domain

The domain of a function is the complete set of possible values of the independent variable.
For example, in the function f(x) = x², the domain consists of all real numbers because any
real number can be squared.
However, for functions like g(x) = 1/x, the domain excludes x = 0 because division by zero is
undefined.

Definition of Range

The range of a function is the set of all possible output values.


For instance, in the function f(x) = x², the range includes only non-negative values (y ≥ 0)
because squaring any real number cannot produce a negative result.
In contrast, for a function like h(x) = sin(x), the range is limited between -1 and 1.

How to Determine Domain and Range

To determine the domain, one must look for values of x that cause the function to be
undefined, such as division by zero or square roots of negative numbers.
To determine the range, we analyze the function's behavior and output values.
Graphing the function is a common method used to visually identify the domain and range.

Applications of Domain and Range

1. **Engineering**: Used in designing control systems where input-output relations are


critical.
2. **Physics**: Applied in motion equations, where domain represents time constraints and
range shows displacement.
3. **Computer Science**: Essential in defining valid inputs for algorithms and data
structures.

Conclusion

Understanding domain and range is fundamental in mathematical analysis.


These concepts help in solving real-world problems where input and output relationships
matter.
By mastering domain and range, students and professionals can enhance their problem-
solving skills in various scientific and technological fields.

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