Question

which of these choices describes the given graph?

a. function only
b. neither a function nor a relation
c. relation only
d. both a function and a relation

Explanation:

1. Recall definitions: A relation is any set of ordered pairs \((x,y)\). A function is a relation where each \(x\) has exactly one \(y\).
2. Analyze the graph: The graph has points (e.g., \(x = 0\) corresponds to \(y = 3\) and \(y=-3\)), so one \(x\) has multiple \(y\)-values. Thus, it is a relation (since it’s a set of ordered pairs) but not a function (fails the vertical line test).

Answer:

C. relation only