Domain and Range of a Function Calculator

Domain and range of a function calculator finds a function’s domain in the interval and set notation instantly. Additionally, it provides graphs of the function as well as a number line representation of the range and domain.

Domain and range of a function calculator

What does Domain and Range mean?

Domain and Range meant values “X” to produce the output value “Y” in Math. A variable’s probable value range is called a ‘value space.’ The dependent variable’s range set the dependent variable’s range the x-coordinates are changed, and these values are given back. Like a function, it will create the output if the input values are specified.

It’s important to remember that a range is, in a nutshell, the set of values that a function can take as input. Both the set of domains and the set of solutions are called “Replacement sets.”

Domain and Range

The range and domain can be determined by seeing if the determined is specified in the real world. Let’s take a closer look at the descriptions of find domain and range.


The domain of a function contains all potential values that qualify as inputs to a function, or it may be described as the full set of independent complete. The denominator is not zero, and the digit in the square root bracket is favourable. Hence this is the favourable or a function with fractional values, and this is the case.

As a sample, find the domain of the function F is set to the letter A, which indicates that “India, Pakistan, Australia, and Sri Lanka” is its scope.

How to Determine a Function’s Domain of Application?

When figuring out the domain, we only need to consider the values of the independent variables that can be used in the above formula (i.e., no zeros or negative signs inside the square root).
Most of the time, all real numbers (R) are thought to be the domain of a function. However, there are several limitations. They’re:

  • The domain is the mixture of all real numbers when the function is of the kind 2x + 5 or f2 – 2.

  • The set of all real values except 1 is the domain of the function f(x) = 1/(x – 1) when supplied.

  • For example, f(x) = 3x + 4, x = 2 - x - 12 is an example of an interval-specific function. x accepts values in the range of 2–12. (i.e. domain).

  • A function’s domain is the set of values for which it can’t be defined.


The collection of all potential values that may be determined for a dependent variable is referred to as a function’s range.

Example: F function ranges from 1983, 1987, 1992, and 1996. In the end, the whole of set B is called it’s codomain. This collection has all of the results of the function. As a result, every real-valued function has a set of real numbers as a codomain. Set B is the function F’s codomain.

Finding the Function’s Range

For example, let’s say we have the following function y = f (x).

  • The function’s range is the range of all the y values, from 0 to 1.

  • Replace all possible values of x in the provided statement to determine whether or not it is positive, negative, or equal to other numbers.

  • Calculate the smallest and largest values of y

  • Afterward, create a graph depicting the same.


The codomain of a relationship or function is the collection of all conceivable outcomes. In some cases, the range of the function is also the codomain. There’s a problem, though, with this statement.

For example, “It is feasible to restrict the range (in this case, the output of a function) by redefining its codomain,” which is intriguing. For instance, the set of all positive integers or all negative real numbers must be the codomain of f(x). A positive integer must be the function’s output in this situation, and the domain must be restricted correspondingly.

To date, functions have been denoted using uppercase characters, but this is increasingly becoming the norm. f(a) Equals f(b) if f is a function from A to B and (a,b) f. Under f, b is referred to as the “Image” of a, and an is referred to as the “Preimage” of b’s “Image.”


In Math, a range is the set of values a function can take as input. A variable’s probable value range is called a ‘value space’. The values set the range of the dependent variable the function gives back after changing its x-coordinates.

Graph-free domain and range determination

When reading from a graph, determining the domain and range is much simpler (but we must make sure we zoom in and out of the graph to see everything we need to see). Therefore, We may not always have access to graphing tools, and drawing a graph typically requires us to know about discontinuities before we can even begin.

As previously said, the most essential items to look for are:

  • The square root symbol does not include any negative numbers.

  • The denominator (bottom) of a fraction does not include any zeros.

Domain and Range By Graph

If the graph of a function is available, determining its domain and range is a breeze. The set of x and y values represented by the graph serves as the defining factor for the graph’s domain, as well as its range. Keep the following points in mind when writing the domain and range from a graph.

  • Check to see if the graph has a straight vertical line. In this case, it is not a function, and the domain and range are not often specified.

  • It is necessary to use coordinates that fall outside of the graph’s domain and range to fill in any gaps that may exist there.

  • A vertical asymptote means that the x-value in the domain should not be there.

  • There should be no x value in the range if the horizontal asymptote is present.

  • The domain and range of the graph are different if the graph is split apart. These sets and intervals are grouped by the “Union” sign ().

  • A curve that ends with an arrow indicates that it should continue in that direction.

After the result

The graph won’t show any x-values that are in the range (The two curves may be drawn in any direction because of the arrows).

The graph covers all y-values higher than or equal to or equal to 0. (see there is no part of the curve that is below the y-axis). It means that the range is [0, ].

Important Notes on Domain and Range:

  1. A function’s domain and range are the set of all conceivable inputs and outputs.

  2. Function y = f(x) has a domain and a range, which are defined as domain= x (x-R), range= x-Domain.

  3. Algebraic or graphical methods can determine the function’s range and domain.

Domain and Range of Trigonometric Functions

The plots of the sine and cosine functions are shown in the graphic that can be found further down the page. Keep in mind that the values of the functions are specified for all real numbers and swing between -1 and 1. As a result, the sine and cosine functions have the following values:

  • The set R serves as the functions’ domain.

  • Functions have a range of [-1, 1].

The following table has a presentation of all of the trigonometric functions:

Trigonometric Functions Domain Range
Cosθ (-∞ +∞) [-1, +1]
Sinθ (-∞, + ∞) [-1, +1]
Cotθ r - nπ (-∞, +∞)
Tanθ r - (2n + 1)π/2 (-∞, +∞)
Cosecθ r - nπ (-*, -1] u [+1, +**)

Range of a Function Calculator with Steps

These easy procedures show us how to determine the domain and range of any real-valued function. Follow these steps to find the domain of the function calculator in a specific way to figure out how to solve the domain and range. Take any function with an absolute value as an example.

  • Find a meaningful value for x in the actual world.

  • The domain has all the real numbers, except for the one that doesn’t make sense.

  • If you change the x and y values in both directions, you can do the inverse function.

Again, we need to know the real values to get outputs that mean something. The range includes all real numbers, except those for which you are not getting output.

Determine the Domain and Range of a Real-Valued Function

  • You can use any linear function that has a real-valued coefficient.

  • As far as we’re concerned, real functions are those that never end in any direction.

  • Any real integer should be put into the function and used to check the output.

In this case, all real numbers are in the domain and range.


Find a meaningful value for x in the actual world. Determine the domain and range of any real-valued function. The range includes all real numbers, except those for which you are not getting output. Follow this domain calculator with steps to find a specific way to solve the problem.

Frequently Asked Question - FAQs

1 - Are domain and codomain different things?

It is the difference between the domain and the codomain in mathematics: the domain is a function’s inputs, and the codomain is its outputs.

2 - What are a function’s natural range and domain?

All of a function’s possible inputs and outputs are its natural domain and range.

3 - How do you determine the function’s range?

The set of all real numbers is usually thought of as the domain of a function. We can, however, remove from the domain set the values for which the given function is undefined for a certain function.

4 - How do you find the domain and range on a calculator?

Enter data into the input box and press the calculate button to get the results.

5 - Do you know the three kinds of domains?

Cognition, emotion, and motor control comprise the three major components of learning. Each domain has numerous stages of learning that evolve from more fundamental, surface-level learning to more complicated, deeper-level learning.

6 - What’s the simplest method to express a function’s parameter range in writing?

You can ascertain the function’s scope by translating it into g(x) form and then identifying its domain set (y). The supplied function f has a range of values like this (x).

7 - What if range and codomain are the same?

The range can’t be bigger than the codomain, but it can be less than that value.

8 - What is the data set’s scope?

This is the difference between the highest and lowest values in the data collection. For example, if the supplied data set is 2,5,8,10,3, the range is 8 – 2 = 10 – 2. It is also possible to think of the range in the difference between the highest and lowest observations.

9 - How are a domain and a range different from each other?

Domain and range are always written from left to right or from bottom to top of the graph, going from smaller to larger values or from left to right.

10 - What do you mean by an example of a domain?

There are two types of internet addresses: domain names and IP addresses. The IP address “” is used by the domain name google. Com as an example. It’s simpler to recall a person’s name than a long string of digits.

11 - What do you mean when you say “Domain Rules”?

Using a domain rule, you can ensure that your domain values are accurate, consistent, and up to date. A domain rule must be true across all domains for domain values to be seen as correct and in line with business needs.

12 - What is a domain name?

Dots split most domain names into two or three distinct components. When read from right to left, the parts of a domain name can be read from most general to most specific. The top-level domain (TLD) is the part of a domain name immediately following the last dot (TLD).

13 - What does the mathematical term “Domain” mean?

The function’s domain is the set of all possible inputs. This function’s domain would include all real numbers except x = 0.

14 - What’s the secret to finding a good range?

Sort your data collection from lowest to highest values. Take the lowest value and subtract it from the highest.

15 - Is range always a great thing?

No, because the range formula subtracts the lowest number from the highest number, the answer is always either zero or a positive value.


The values form the domain and range X and Y can take, respectively. The y values depend on the x values. Remember, make it easier. It’s written down as “Y=F” (X). Knowing what a domain and range are is important to solve more difficult arithmetic problems.

You should consult your textbook or your teacher if unsure of the ingredients or the sequence. A mathematical expression of the function will be generated automatically.

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