Courses

Courses for Kids

Free study material

Talk to our experts

1800-120-456-456

Domain and Range Calculator: Free Online Maths Tool

Q: 5. What is the domain and range of a linear function?

A linear function, f(x) = mx + b, has a domain of all real numbers (-∞, ∞) because you can substitute any real number for x. Its range is also all real numbers (-∞, ∞) because the output can take on any real value.

Q: 6. How do you find the domain and range from a graph?

To find the domain from a graph, look at the x-values where the graph exists. The range is found by examining the y-values covered by the graph. Consider whether the endpoints are included (closed circles) or excluded (open circles).

Q: 7. What is the domain and range of a square root function?

For a square root function like f(x) = √x, the domain is all non-negative real numbers (x ≥ 0) because you cannot take the square root of a negative number. The range is also y ≥ 0.

Q: 8. What are some real-world applications of domain and range?

Domain and range have many real-world applications. For example, in physics, the domain might represent time, and the range represents the distance traveled. In economics, the domain might be the number of units produced, and the range is the total cost. Understanding them is important in various fields.

Q: 9. How to find the domain and range of a rational function?

For rational functions (fractions of polynomials), the domain excludes any values of x that make the denominator zero. Finding the range can be more complex and often involves analyzing asymptotes and the behavior of the function as x approaches infinity or negative infinity.

Q: 10. What is the difference between domain and codomain?

The domain is the set of all possible inputs for which a function is defined. The codomain is the set of all possible outputs; the range is a subset of the codomain representing the actual outputs the function produces. The codomain is a broader concept, encompassing all potential outputs.

Latest Updates

Book Free Demo :

One-to-One Learning - Any Topic, Any Time

How to Find Domain and Range of a Function with Steps & Examples

Domain and Range Calculator – Free Online Tool with Formula, Steps & Examples

Domain and Range Calculator

What is Domain and Range Calculator?

The Domain and Range Calculator is a free online maths tool developed to instantly find the set of all possible input values (domain) and output values (range) of a function, graph, or data set. Simply enter your function expression, such as x^2, 1/x, sin(x), or a data set like 3, 6, 5, 9, and get fast, accurate results with stepwise explanations. This calculator is widely used by students and teachers to check questions on algebra, graphs, or mapping data – making mathematical analysis faster and more reliable.

Formula or Logic Behind Domain and Range Calculator

Domain: The set of all possible input values (x) for which a function is defined.
Range: The set of all possible output values (f(x) or y) a function can produce from its domain.

General rules:

For algebraic functions: Exclude any x that causes division by zero, square roots of negatives, or other undefined operations (e.g., ln(x) where x ≤ 0).
For trigonometric functions: Look for x that makes the function undefined (such as tan(x) at odd multiples of π/2).
For a data set: Domain = all unique x-values; Range = all unique y-values.

The Domain and Range Calculator applies these rules instantly and, for functions, tries to analyze both algebraically and by sampling values.

Domain and Range of Common Functions

Function / Data	Domain	Range
f(x) = x²	All real numbers	y ≥ 0
f(x) = 1/x	x ≠ 0	y ≠ 0
f(x) = √x	x ≥ 0	y ≥ 0
f(x) = sin(x)	All real numbers	-1 ≤ y ≤ 1
Data: 3, 6, 5, 9	3, 5	6, 9

Steps to Use the Domain and Range Calculator

Enter the required function (e.g., x^2, sqrt(x), 2x+5) or data values (e.g., 3, 6, 5, 9)
Click on the 'Calculate' button
Get instant results for Domain and Range with brief explanations

Why Use Vedantu’s Domain and Range Calculator?

Vedantu’s domain and range finder is designed for instant accuracy, mobile-friendly use, and student-centric convenience. You get not just the answer, but also the reasoning or restrictions explained. It supports a variety of maths inputs (functions, equations, datasets), provides step-by-step logic, and is trusted by lakhs of school/college students and educators across India. Use it for checking answers, last-minute exam prep, or to build intuition about algebra and graphs.

Real-life Applications of Domain and Range Calculator

The Domain and Range Calculator aids in a huge variety of academic and practical tasks:

Analyzing graphs in algebra, trigonometry, or calculus
Verifying data sets for science/engineering projects (mapping input to output)
Validating function restrictions in programming or computer algorithms
Checking mathematical models in Physics or Economics, such as motion equations or demand curves
Examining allowed values in statistics, statistics frequency tables, and real-world datasets

Make your study or project workflow faster and clear whether you are prepping for board exams, JEE, Olympiads, or doing classroom/lab analysis.

Want to expand your maths toolkit? Explore related topics on: Prime Numbers, Factors of Numbers, Algebra Topics, Union of Sets, Quadratics.

FAQs on Domain and Range Calculator: Free Online Maths Tool

1. What is the domain and range of a function?

The domain of a function is the set of all possible input values (x-values) for which the function is defined. The range is the set of all possible output values (y-values) that the function can produce. Understanding domain and range is crucial for graphing and analyzing functions.

2. How do I find the domain of a function?

To find the domain, identify any values that would make the function undefined. This includes division by zero, even roots of negative numbers, and logarithms of non-positive numbers. Exclude these values from the set of all real numbers to determine the domain. For example, the domain of f(x) = 1/x is all real numbers except x = 0.

3. How do I find the range of a function?

Finding the range involves determining all possible output values (y-values) the function can produce. This often involves analyzing the function's behavior, its graph, or solving for y in terms of x. For example, the range of f(x) = x² is y ≥ 0 because the square of any real number is non-negative.

4. What is the domain and range of a quadratic function?

The domain of a quadratic function, like f(x) = ax² + bx + c, is all real numbers (-∞, ∞). The range depends on whether the parabola opens upwards (a > 0) or downwards (a < 0). If it opens upwards, the range is y ≥ the y-coordinate of the vertex. If it opens downwards, the range is y ≤ the y-coordinate of the vertex.

5. What is the domain and range of a linear function?

A linear function, f(x) = mx + b, has a domain of all real numbers (-∞, ∞) because you can substitute any real number for x. Its range is also all real numbers (-∞, ∞) because the output can take on any real value.

6. How do you find the domain and range from a graph?

To find the domain from a graph, look at the x-values where the graph exists. The range is found by examining the y-values covered by the graph. Consider whether the endpoints are included (closed circles) or excluded (open circles).

7. What is the domain and range of a square root function?

For a square root function like f(x) = √x, the domain is all non-negative real numbers (x ≥ 0) because you cannot take the square root of a negative number. The range is also y ≥ 0.

8. What are some real-world applications of domain and range?

Domain and range have many real-world applications. For example, in physics, the domain might represent time, and the range represents the distance traveled. In economics, the domain might be the number of units produced, and the range is the total cost. Understanding them is important in various fields.

9. How to find the domain and range of a rational function?

For rational functions (fractions of polynomials), the domain excludes any values of x that make the denominator zero. Finding the range can be more complex and often involves analyzing asymptotes and the behavior of the function as x approaches infinity or negative infinity.

10. What is the difference between domain and codomain?

The domain is the set of all possible inputs for which a function is defined. The codomain is the set of all possible outputs; the range is a subset of the codomain representing the actual outputs the function produces. The codomain is a broader concept, encompassing all potential outputs.

11. Can the domain and range be infinite?

Yes, the domain and range can be infinite. For instance, linear functions often have both a domain and range of all real numbers (-∞, ∞), representing an infinite set of possible inputs and outputs.