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.
To determine if the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function, we can use the vertical line test. The vertical line test states that for a relation to be a function, no vertical line should intersect the graph of the relation more than once.
Looking at the points given in the relation, we can plot them on a graph.
The first point is (-6, -2), so we plot a point at (-6, -2).
The second point is (-2, 6), so we plot a point at (-2, 6).
The third point is (0, 3), so we plot a point at (0, 3).
The fourth point is (3, 5), so we plot a point at (3, 5).
After plotting these points, we can draw a vertical line anywhere on the graph and observe if it intersects the graph more than once. By doing this, we can see that for every vertical line we draw, it only intersects the graph once. Therefore, no vertical line intersects the graph of this relation more than once.
Since no vertical line intersects the graph more than once, we can conclude that the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} passes the vertical line test. Therefore, this relation is a function.