Cue the memories from the Advanced Math classes we took in high school. Endless hours were spent trying to understand the relative functions.

And what exactly is the distinction between domain and range? Domain and range are a part of solving problems with functions that fall under physical science.

The domain and range of a function play a critical role in solving the problem.

## Key Takeaways

- A domain represents all possible input values for a function, while a range signifies the corresponding output values.
- Understanding the domain and range of a function aids in graphing and solving mathematical problems.
- Real-world applications of domain and range include predicting stock market trends and optimizing engineering designs.

## Domain vs Range

In mathematics, the domain of a function is the set of all possible input values for the process, while the range is the set of all possible output values. For example, consider the function f(x) = x^2. The domain is all real numbers, but the range is only the set of non-negative real numbers.

The domain of a function is the set representation of the values for which the mathematical function is defined. A part is referred to as the independent variable in any given process.

Put; the domain refers to the input values that the function can have.

The range of a function is the set representation of the values for which the mathematical process can take presence. Any ‘s range part is considered a dependent variable, unlike its counterpart.

The range contains the outputs of a given function after it is solved mathematically to obtain the solution.

## Comparison Table

Parameters of Comparison | Domain | Range |
---|---|---|

Definition | It can be referred to as the acceptable set of inputs. | The range of any function is defined as the set of resulting values. |

Dependency | It consists of independent variables. | It consists of dependent variables, unlike its counterpart. |

Axis | The mathematical domain of any function is measured alongside the X-axis. | The range of a function is measured alongside the Y-axis to obtain the values. |

Consists of | It consists of all the probable input values. | All probable output values are recorded in the set. |

Example | The time between sunrise and sunset. | Elevation of the sun at any given point. |

## What is Domain?

Domain refers to the intangible set of values that defines a mathematical function. It is a part of relations and functions.

It must be noted that a function’s domain is not a property of the function; instead, it is the definition of the given function.

Domains are independent variables that cannot be influenced by any other element used in the calculation.

It can be described as the input values that a function has. Furthermore, all the parts are limited to the domain’s subsets.

They are used about the set of inputs that the function can accept.

Domains are measured alongside the X-axis in a graph when computing the values. The X-axis lies horizontally in any given graphical representation.

The domain’s value differs depending on the type of function being solved. Every mathematical problem has a varying set of domain values.

The domain values for the cosine function include all real numbers over and below zero. The set also consists of the value of zero. However, the domain values for a square root cannot be lesser than zero.

The domain of a function is written as f: x->y, wherein the part of f is x.

A real-life example would be the time between sunrise and sunset; this period includes all the domain values.

## What is Range?

The range of the function includes the values of a mathematical function that can exist. It sums up the output values of the process.

The range of a function is a dependent variable. It cannot exist individually.

The domain of a function plays a critical part in helping determine the set values of the range. The process solutions that are solved mathematically consist of the range set of the said function.

The range of a function is associated with the image of the given process and the codomain of the process.

A dependent variable’s value is derived using mathematical applications and mathematically solving the function.

The function’s range is represented in the Y-axis. The Y-axis of a graph is located vertically in any given quadrant.

The value of the range cannot be calculated without the knowledge of the set values of the domain. When the domain value of a function y=f(x) is x, y would be considered as its range.

One of the most straightforward examples of a real-life range is the sun‘s altitude on the axis from zero to the maximum elevation on a given latitude and time.

The range is a codependent variable that consists of the outputs of the given or mentioned function.

## Main Differences Between Domain and Range

- Domain and range are a part of mathematical relations and functions. The domain holds the inputs within it, whereas the range is the sum of all the outputs.
- The domain is independent, while the range depends on the former to find the values.
- The domain is situated alongside the horizontal x-axis, while the range is located on the y-axis that is represented vertically.
- The domain includes what is included in a function. Meanwhile, the range talks about the function’s result in lieu of the domain values.
- The rising and the sun’s setting are examples of the domain. The sun’s altitude at a given point in time is its resultant range.

**References**

- https://link.springer.com/content/pdf/10.1007/0-306-47204-X.pdf#page=361
- http://pbc.biaman.pl/Content/24034/1990%20nr%202.pdf#page=73

Last Updated : 11 June, 2023

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.