# Domain and Range Calculator

## Calculate domain and range step by step

The calculator will find the domain and range of the single-variable function.

Enter a function of one variable:
Enter an interval:
Required only for trigonometric functions. For example, [0, oo) or (-2, 5pi]. If you need oo, type inf.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

The Domain and Range Calculator is a tool designed to help you determine the domain and range of a function. Whether you're studying calculus, algebra, or another discipline, our calculator gives you an accurate understanding of the fundamental concepts of domain and range.

## How to Use the Domain and Range Calculator?

• ### Input

Enter the function you want to analyze into the provided input field. Make sure to use proper mathematical notation and symbols.

• ### Calculation

Click the "Calculate" button to process the function. Our calculator will analyze the function and determine its domain and range.

• ### Result

The calculator will display both the domain and the range of the function. The domain consists of all possible x-values for which the function is defined, while the range consists of all possible y-values that the function can produce.

## What Is Meant by Domain and Range?

Domain and range are fundamental concepts that give insight into the behavior of functions. They help determine the values for which the function is valid and the values it can produce as output. Understanding domain and range is essential for interpreting functions and their properties.

Domain

The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces meaningful results. In other words, it represents the range of values that the function can take and produce a valid result out of. A function may have restrictions on its domain due to mathematical limitations or practical considerations.

The domain of a function $f$ is often denoted as $D(f)$ and can be expressed using interval notation, inequalities, or other relevant mathematical representations.

Range

The range of a function is the set of all possible output values (y-values) that the function can give within its domain. It represents the set of values that the function can produce as its output. The range gives an idea of the vertical extent of the graph of the function and the variety of its output values.

The range of a function $f$ is denoted as $R(f)$ and can be described using interval notation, inequalities, or other appropriate mathematical forms.

Example

Consider the function $f(x)=\sqrt{x}$, which represents the square root of $x$. The domain of this function would be all non-negative real numbers, i.e. $x\ge0$, as the square root is undefined for negative values. The range also consists of all non-negative real numbers, i.e. $f(x)\ge0$, since the square root of any non-negative number produces a non-negative result.

## Why Choose Our Domain and Range Calculator?

• ### Correct Results

Our calculator provides accurate calculations of both the domain and the range of functions. You can be sure that the results will be accurate and useful for your analysis.

• ### User-Friendly Interface

Our calculator offers an intuitive interface that will guide you through the entire process. You don't need to be a math expert to use it effectively.

• ### Educational Tool

Whether you are a student trying to understand the concept of domain and range or an educator teaching it, our calculator will assist you. It helps to visualize and understand the meaning of domain and range.

• ### Accessibility

Whether you're using a computer, tablet, or smartphone, you can conveniently use the calculator wherever you are.

### FAQ

#### What is the domain of a function?

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined and gives meaningful results.

#### What is the range of a function?

The range of a function refers to the set of all possible output values (y-values) that the function can produce within its domain.

#### How do I use the Domain and Range Calculator?

Using our calculator is simple. Input the function you want to analyze, click the "Calculate" button, and our calculator will determine the domain and the range of the function.

#### What if a function has restrictions on its domain?

Our calculator takes into account any domain restrictions and correctly finds the domain and the range.