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

Verified step by step guidance

1. Identify the given relation on the graph. The graph shows a set of points and arrows indicating the relation.
2. Check if each input (x-value) corresponds to exactly one output (y-value). If any x-value corresponds to more than one y-value, the relation is not a function.
3. In the graph, observe that the x-value -2 corresponds to the y-value -4. However, there are arrows indicating that other x-values also map to y-values.
4. Determine the domain of the relation. The domain is the set of all possible x-values. From the graph, identify the range of x-values covered by the relation.
5. Determine the range of the relation. The range is the set of all possible y-values. From the graph, identify the range of y-values covered by the relation.

Key Concepts

Function Definition

A function is a specific type of relation where each input (or x-value) corresponds to exactly one output (or y-value). This means that for any given x, there cannot be two different y-values. 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, the relation 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 involves analyzing the graph or the set of ordered pairs to see which values are included. For example, if a graph extends infinitely in the x-direction, the domain may be all real numbers.

Graph Interpretation

Interpreting a graph involves understanding the visual representation of a relation. This includes identifying key points, such as intercepts and vertices, and recognizing the overall shape and direction of the graph. In the provided image, the point (-2, -4) is significant, and the arrows suggest the behavior of the relation as it extends in the horizontal direction, which is crucial for determining the function status.