While relations and functions are concerned, it may be important to know about the domain and the range which probably have a great significance in the entire scene.

## What is range?

As you may know already, functions and relations take up inputs and outputs. The inputs are the values entered and the output is undeniably the result obtained. The set of probable outputs for the considerable relation or function is known to be the range of that relation or function. For instance, consider this function defined below that is based on the fact that the input is taken up and then raised to its third power.

When represented in the form of an equation, it would be y = x^3. When the input values for this function are given:

{-2, -1, 0, 1, 2}

The corresponding outputs for these inputs could be obtained by placing these values in the given equation for x. For example, consider that we choose to input -2, we would have the equation like: y = (-2) ^3 = -8. Here, since the output is -8, -8 would be the range value. When we will obtain outputs for all the corresponding domain values, we’d get the entire list of the range set. Based on the inputs given, the corresponding set of range is likely to be: {-8, -1, 0, 1, 8}.

## Notation of range

Ranges can be of course written out in words as mentioned-above, but considering mathematical preciseness, they are also known to be written in interval notations or using inequalities.

As an inequality it would be written as:

f(x) ≥ x^{2}

This would be read as “the function f(x) is a value that is always supposed to be either greater than zero or equal to zero.”

In an interval notation, the same function is said to have a range of:

[0, +∞)]

As per this notation the range values could be any numbers from zero to positive infinity. Square brackets mean that the range also includes zero and infinity along all the elements.

## How to find the range?

- The range of any considerable relation or function actsually a spread of possible outputs for the same. In other words, the list of possible y values, ranging from the minimum to the maximum.
- Substitute various values of x into the relation to see what happens.
- Make sure that you look out for both minimum and maximum values of y.
- Make out a graph.

This way you can easily obtain the range for any relation or function.