Domain and Range of a Function

Defining Domain and Range

The domain of a function is essentially the set of “input” values, i.e., the values that can be put into a function.
Remember to think of functions as machines: whatever you put in is the domain, and whatever comes out is the range.
The range of a function refers to the set of “output” values or possible results you can get from a particular function.
The domain and range aren’t necessarily the same. Depending on the function, the range may be a subset of the domain.
Domain and range are often described or visualised using graphs, with the x-values representing the domain and the y-values representing the range.

Common Mistakes with Domain and Range

Not all values may be suitable as input for a function. For example, in a function where the input number is the denominator, it cannot be 0, as division by zero is undefined.
When considering domain or range for a function involving a square root, remember that the result must be a real number. Hence, the number under the square root cannot be less than 0.
For functions involving a fraction, remember that the denominator cannot be 0 as this would make the function undefined.

Tips on Finding Domain and Range

To find the Domain: Look for values that you can’t use as they would make the function undefined.
To find the Range: Look for values that the function just won’t output no matter what value you put in.
In the context of graphs, for the domain, ask what x-values are covered by the graph; and for the range, ask what y-values are covered by the graph.