Functions have a domain and range and can be found in two ways. If the function is graphed, the domain and range can be identified from the picture, or the domain and range can be found algebraically with some reasoning.

##### Domain

The domain of a function is the set of all x-values that have a y-value associated with them. In other words, it is the set of all “inputs” that will receive an “output”.

Examples

**Find the domain of y = x.**

The graph of y = x is shown to the right. We can see that it is defined for all x-values because the line will continue to infinity. Thus, the domain of y = x is all real numbers.

**Find the domain of **

We do not have the graph but there are properties of the square root function that we can use in order to determine the domain. In order to square root a number, it must be greater or equal to 0. This tells us that y only has a value when x is greater or equal to 0. Therefore the domain is x must be greater or equal to 0.

##### Range

The range of a function is the set of all y-values that have a corresponding x-value. In other terms, it is the set of all “outputs” of a function that have an “input”.

Example

The graph y = x^{2} is the standard parabola as shown to the right. We can see that the graph has y-values that continue to positive infinity but have a minimum of 0 at the origin. There are no points that have a y-value less than 0 and so the range is y must be greater or equal to 0.

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This article was written for you by **Jeremie**, one of the tutors with Test Prep Academy.