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

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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 has points (e.g., \(x = 0\) corresponds to \(y = 3\) and \(y = -3\)). For \(x = 0\), there are two \(y\)-values, so it fails the vertical line test (a function’s graph must pass this test: no vertical line intersects the graph more than once).
3. Conclusion: The graph is a relation (since it consists of ordered pairs) but not a function (due to multiple \(y\)-values for one \(x\)-value). Thus, it is a relation only.

Answer:

C. relation only