Find the range of a graph calculator

$$ f : x \mapsto 1 + {1 \over x}, x \in \mathbb{R}, x \ne 0 $$

From the graph, $y$ can be any real value except $1$.

The range in set-builder notation is $$ R_f = \{ y \in \mathbb{R} \phantom{.} | \phantom{.} y \ne 1\} $$

The range in interval notation is $$ R_f = ( -\infty, 1) \phantom{.} \cup \phantom{.} (1, \infty) $$

An alternative presentation in interval notation is $$ R_f = \mathbb{R} \backslash \{1 \} $$

Example (with restricted domain)

$$ g : x \mapsto x^2 - 2x - 2, \phantom{000} x \in \mathbb{R}, x > -1 $$

From the graph, the smallest value of $y$ is $-3$ (minimum point).

The range in set-builder notation is $$ R_g = \{ y \in \mathbb{R} \phantom{.} | \phantom{.} y \ge -3 \} $$

The range in interval notation is $$ R_g = [-3, \infty) $$

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:

• 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

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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.

Your input: find the domain and range of $$$f=\frac{1}{x - 1}$$$

Domain

$$$\left(-\infty, 1\right) \cup \left(1, \infty\right)$$$

Range

$$$\left(-\infty, 0\right) \cup \left(0, \infty\right)$$$

Graph

For graph, see graphing calculator.

How do you find the range in a graph?

What is the range of a function calculator?

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