The relationship between domain and range is fundamental to understanding functions in mathematics.
Domain: The Input Values
The domain of a function refers to all the possible input values, or x-values, that the function can accept. It's like the set of ingredients you can use in a recipe.
Range: The Output Values
The range of a function encompasses all the possible output values, or y-values, that the function can produce. It's like the set of dishes you can create from those ingredients.
The Connection: Input and Output
The relationship between domain and range lies in the fact that the function maps each element of the domain to a specific element in the range. Every input value from the domain has a corresponding output value in the range.
Example:
Consider the function f(x) = x².
- Domain: All real numbers (because you can square any real number).
- Range: All non-negative real numbers (because squaring a number always results in a non-negative value).
Key Points:
- The domain and range are essential for understanding the behavior of a function.
- The domain defines the set of inputs that the function can accept.
- The range defines the set of outputs that the function can produce.
