Domain Range 70C48C

1. **Problem Statement:** Define the concepts of domain and range in mathematics. 2. **Definition of Domain:** The domain of a function is the set of all possible input values (usually $x$) for which the function is defined. 3. **Definition of Range:** The range of a function is the set of all possible output values (usually $y$) that the function can produce from the domain. 4. **Explanation:** - The domain tells us what values we can plug into the function. - The range tells us what values we can get out of the function. 5. **Example:** For the function $$f(x) = \sqrt{x}$$, - The domain is all $x \geq 0$ because square roots of negative numbers are not real. - The range is all $y \geq 0$ because square roots produce non-negative results. 6. **Summary:** - Domain: all valid inputs. - Range: all possible outputs. This understanding helps in analyzing and graphing functions effectively.