Question

which of the choices describes the given graph?
a. function only
b. relation only
c. both a function and a relation
d. neither a function nor a relation

Explanation:

1. Define Relation and Function: A relation is any set of ordered pairs \((x,y)\). A function is a relation where each \(x\)-value has exactly one \(y\)-value.
2. Analyze the Graph: The graph contains points (e.g., check for repeated \(x\)-values). If an \(x\)-value maps to multiple \(y\)-values (fails the vertical line test), it is not a function. Since it is a set of ordered pairs, it is a relation, but not a function (due to multiple \(y\)-values for at least one \(x\)). Thus, it is a relation only.

Answer:

B. relation only