# Describe Domain And Range

The domain of a function is the set of all possible inputs for the function and the range of a function is the set of all its outputs.

## Answer: A domain is ‘all the values’ that go into a function and the range of a function in algebra is the set of all its outputs.

Domain and range are described as follows.

## Explanation:

A **domain **is ‘all the values’ that go into a function. The domain of a function is all the possible values of the independent variable x, for which y is defined.

The **range **of a function in algebra is the set of all its outputs. It is also known as a codomain.

The domain of a function is all the possible values of the independent variable x, for which y is defined. The range of a function is all the possible values of the dependent variable y.

On a function graph, the set of values towards the direction of the x-axis is the domain whereas, the set of values towards the direction of y-axis is termed as range.

In a given ordered pair (x,y) the domain is defined as the set of all first elements of ordered pairs (x-coordinates) and the range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range.

Let's take an example to understand domain and range.

The function y=a^{x}, a≥0 is defined for all real numbers.

Hence, the domain of the exponential function is the entire real line.

The exponential function always results in a positive value.

Thus, the range of the exponential function is of the form y=|ax+b| is {y∈R|y>0}.

Thus, Domain = {R}, Range = (0,∞)

{R} signifies the set of real numbers.

**Example: 2 ^{x}**

Look at the graph of this function shown below.

Observe that the value of the function is closer to 0 as x tends to ∞, but it will never attain the value 0

**Domain**

The domain of the function is the set {R}

**Range**

The exponential function always results in positive real values.