UpStudy Free Solution:

To determine which graph represents a function, we need to ensure that each input (x-value) has exactly one output (y-value). This can be checked using the vertical line test: if a vertical line intersects the graph at more than one point, then the graph does not represent a function.

- The first graph has multiple y-values for \(x = - 1\) and \(x = 1\), so it does not represent a function.

- The second graph has each x-value corresponding to exactly one y-value, so it does represent a function.

- The third graph has multiple y-values for \(x = - 2\), so it does not represent a function.

Therefore, the second graph shows a set of ordered pairs that represent a function.

Supplemental Knowledge:

A function is a relation in which each input (x-value) has exactly one output (y-value). This means that for a graph to represent a function, no vertical line should intersect the graph at more than one point. This is known as the Vertical Line Test.

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