Note: Your teacher will grade your responses to the following questions to ensure that you receive proper credit for your answers.
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.
In order to determine if the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function, we need to use the vertical line test. The vertical line test states that if a vertical line can intersect the graph of a relation at more than one point, then the relation is not a function.
Looking at the graph, we can imagine drawing vertical lines at different x-values. If any vertical line intersects the graph at more than one point, then the relation would not be a function.
Starting from the left, if we draw a vertical line at x = -6, it intersects the graph at the point (-6, -2). This is the only point of intersection for this vertical line.
Moving to the right, if we draw a vertical line at x = -2, it intersects the graph at the point (-2, 6). This is again the only point of intersection for this vertical line.
Continuing to the right, if we draw a vertical line at x = 0, it intersects the graph at the point (0, 3). Once again, this is the only point of intersection for this vertical line.
Finally, if we draw a vertical line at x = 3, it intersects the graph at the point (3, 5). Like before, this is the only point of intersection for this vertical line.
Since every vertical line we draw intersects the graph at only one point, we can conclude that the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} passes the vertical line test. Therefore, it is a function.