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 online domain and range calculator with steps finds domain and range for a function in a couple of clicks. Examines the range in which the domain of a certain mathematical function exists. Not only this, but you will also get results in proper set interval notations.
What Is the Domain?
Particular set of values that help to define a function after they are put in it by our domain calculator.
What Is the Range?
The set of values that the function yields after the domain values are put in it.
Example:
Consider the figure below:
In the following figure:
- D is not concerned with any of the range entities, so it is not considered as the domain of the function
- Likewise, the number 2 is not linked with any domain element, yielding it as an odd man out for range
In actual, calculating domain and range of the function will let you investigate the behaviour
How to Find Domain and Range of a Function?
Go through the example below to better understand how to find the domain of a function along with its range!
Statement:
Find domain and range of the graph function given as under:
$$ y=\dfrac{x+3}{10-x} $$
Solution:
Domain:First, look for the value of x that will make the denominator zero. In our case, it is 10, such that;
$$ 10-x = 10-10 = 0 $$
So 10 is the number that undefines the whole expression. This is why it is not included in the domain.
Range:Solving for x:
$$ y=\dfrac{x+3}{10-x} $$
$$ y\left(10-x\right)=x+3 $$
$$ 10y-xy=x+3 $$
$$ -xy-x=3-10y $$
$$ -x\left(y+1\right) $$
$$ -x=\dfrac{3-10y}{\left(y+1\right)} $$
$$ x=\dfrac{10y-3}{-\left(y+1\right)} $$
Now if you put value of y as -1, it will again make the denominator as zero such that:
$$ x=\dfrac{10y-3}{-\left(\left(-1\right)+1\right)} $$
How Does Domain and Range Calculator Function Work?
Want to calculate domain and range of functions through our domain finder? Follow the guide below!
Input:
- Enter your function and hit calculate to find results
Output:
- Domain and range of the function
Is 7 a Domain or Range?
7 means y=7, and it indicates a straight line equation. Coming to the point, its domain is all real numbers and range is 7 only. For further verification, you may put the expression in the online domain and range calculator with steps to nullify your doubts.
The range of some function is a set, containing all the values that can be obtained by substituting into this function all the valid values of the argument . The range of the function is denoted by .
Illustrate the above with a concrete example. Consider the function , which graph is shown on the figure.
Its easy to mention, that whatever values of argument we would not substitute into the function , the returning value will always be in the range from to . Thus, the range of the function in question is from to .
This fact can be written as follows:
Our online calculator is based on Wolfram Alpha system. The calculator allows to find the range of almost any function.
Domain and Range Calculator is a free online tool that displays the range and domain for the given function. BYJU’S online domain and range calculator tool makes the calculation faster, and it displays the output in a fraction of seconds.
How to Use the Domain and Range Calculator?
The procedure to use the domain and range calculator is as follows:
Step 1: Enter the function in the input field
Step 2: Now click the button “Calculate Domain and Range” to get the output
Step 3: Finally, the domain and range will be displayed in the new window
What is Meant by Domain and Range?
In Mathematics, a domain is defined as the set of possible values “x” of a function which will give the output value “y”. It is the set of possible values for the independent variables. The range of a function is defined as the set of resulting values of the dependent variable. These are the set of output values when the x values are substituted. It is similar that, when the input values are given to the function, it will produce the output.
Also, read: Domain, Codomain and Range of a Function
In short, a domain is defined as the set of values for which the function f(x) is defined, whereas the range is defined as the set of values that the function takes. The domain is called the replacement set, and the range is called the solution set.