Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

Key Concepts

Function Definition

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 every x-value in the domain, there is only one corresponding y-value in the range. To determine if a relation is a function, one can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not 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 is crucial for understanding the behavior of a function. In the given relation, the domain consists of the numbers 4, 9, 13, and 19, while the range includes the outputs 18, 25, 28, and 35.

Mapping Diagrams

Mapping diagrams visually represent the relationship between the domain and range of a function. In these diagrams, arrows indicate how each input is connected to its corresponding output. They help in quickly assessing whether a relation is a function by showing the connections clearly, making it easier to identify if any input is linked to multiple outputs.