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.
The vertical line test is a method used to determine if a relation is a function. In this test, a vertical line is drawn through the graph of the relation. If the line passes through more than one point of the graph at a time, then the relation is not a function, as it would violate the definition of a function where each input corresponds to exactly one output.
Let's apply the vertical line test to the given relation {(-6, -2), (-2, 6), (0, 3), (3, 5)}:
Drawing a vertical line through the graph of the relation, we see that the line only intersects the graph at one point at a time. Therefore, every input (x-coordinate) in the relation corresponds to exactly one output (y-coordinate), and no two inputs share the same output.
Hence, based on the vertical line test, we can conclude that the relation {(-6, -2), (-2, 6), (0, 3), (3, 5)} is a function.