Determine whether each relation defines a function, and give the domain and range. See Examples 1–4. {(2,5),(3,7),(3,9),(5,11)}

Key Concepts

Definition of a Function

A function is a specific type of relation where each input (or domain element) is associated with exactly one output (or range element). This means that for any given x-value, there cannot be multiple corresponding y-values. Understanding this definition is crucial for determining whether a relation qualifies as a function.

Domain and Range

The domain of a relation is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). Identifying the domain and range helps in understanding the behavior of the function and the values it can take. In the given relation, analyzing the pairs will reveal both the domain and range.

Identifying Non-Function Relations

To determine if a relation is not a function, one must look for instances where a single input is paired with multiple outputs. In the provided relation, the presence of the input '3' associated with both '7' and '9' indicates that it does not define a function. Recognizing these patterns is essential for accurate classification.