The domain of a function refers to the set of all possible input values for a given function. In other words, it is the set of values that can be plugged into the function to produce a valid output.
An open interval is a range of values that includes all real numbers between two given endpoints, but does not include the endpoints themselves. It is represented as (a, b), where a and b are the endpoints and are not included in the interval.
A closed interval is a range of values that includes all real numbers between two given endpoints, including the endpoints themselves. It is represented as [a, b], where a and b are the endpoints and are included in the interval.
The type of interval for a function depends on the type of brackets used to represent the endpoints. If the endpoints are represented with parentheses, then the interval is open. If the endpoints are represented with square brackets, then the interval is closed.
The domain of a function is important because it tells us which values can be used as inputs for the function. It also helps us determine the range of the function, which is the set of all possible output values. Understanding the domain can also help us identify any restrictions or limitations on the function, and ensure that we are using it correctly.