What is a defined range in a function?

The defined range of a function is indeed the set of possible output values that the function can produce. When we talk about a function, we first look at the relationship it defines between inputs (often termed the domain) and outputs. The range describes all the values that the function can output based on all permissible inputs from its domain.

For example, if you have a function that relates ( x ) to ( y ) through ( y = x^2 ), and your inputs ( x ) are restricted to real numbers, the outputs ( y ) will be all non-negative values (0 and positive numbers) since squaring any real number cannot yield a negative result. Thus, in this scenario, the range would be from 0 to infinity.

Recognizing that the range focuses solely on the outputs helps distinguish it from the domain, which is concerned with the allowable inputs. Hence, understanding that the defined range identifies the set of values that the function can output is crucial for working with functions in mathematics.