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# Domain and Range Calculator

Write the function in the designated field and the tool will display the domain and range of the function.

Equation:

Equation Preview:

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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.

## References:

From the source of Wikipedia: Domain of a function, Natural domain, Set theoretical notions

From the source of Khan Academy: Domain and range from graph, Intervals