Use the vertical line test to determine if the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function. Explain your response.
A coordinate plane with ordered pairs (-6, -2), (-2, 6), (0, 3) and (3,5) plotted.
To use the vertical line test, we imagine a vertical line being drawn through the graph of the relation. If the vertical line intersects the graph at more than one point, then the relation is not a function. On the other hand, if the vertical line intersects the graph at most one point, then the relation is a function.
In this case, we can see that if we were to draw vertical lines through the points (-6, -2), (-2, 6), and (3, 5), the lines would intersect the graph at only one point each time. However, if we were to draw a vertical line through the point (0, 3), it would intersect the graph at two different points: (0, 3) and (-2, 6).
Therefore, since there exists a vertical line that intersects the graph of this relation at more than one point, the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is NOT a function.