Question

which of the choices describes the given graph?

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

Explanation:

1. Recall the definitions: 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 a point (or points) where an \(x\)-value (e.g., \(x = 6\)) is paired with two different \(y\)-values (the two red dots at \(x = 6\) have different \(y\)-coordinates). So it fails the vertical line test (a vertical line at \(x = 6\) would intersect the graph at two points), meaning it is not a function. But since it consists of ordered pairs (points on the graph), it is a relation. Thus, it is a relation only.

Answer:

B. relation only