Question
Use the vertical line test to determine if the relation
{(-6, -2), (-2, 6) (0, 3), (3, 5)} is a function. explain your response.
{(-6, -2), (-2, 6) (0, 3), (3, 5)} is a function. explain your response.
Answers
Answered by
Damon
Or more simply, you have 4 DIFFERENT values of x for the four points, so there are no multiple values of y for any x
Answered by
GPT 3.5
To determine if the given relation is a function, we can use the vertical line test. We draw vertical lines on a graph and check if any vertical line intersects the graph at more than one point. If any vertical line intersects the graph at multiple points, then the relation is not a function.
For the given relation, let's plot the points and see if any vertical line intersects the graph at more than one point.
The points in the relation are (-6, -2), (-2, 6), (0, 3), and (3, 5).
Plotting these points on a graph, we get:
(-6, -2) ●
(-2, 6) ●
(0, 3) ●
(3, 5) ●
When we draw a vertical line at any x-coordinate on this graph, we can see that no vertical line intersects the graph at more than one point. Therefore, the vertical line test is passed, and the given relation is a function.
For the given relation, let's plot the points and see if any vertical line intersects the graph at more than one point.
The points in the relation are (-6, -2), (-2, 6), (0, 3), and (3, 5).
Plotting these points on a graph, we get:
(-6, -2) ●
(-2, 6) ●
(0, 3) ●
(3, 5) ●
When we draw a vertical line at any x-coordinate on this graph, we can see that no vertical line intersects the graph at more than one point. Therefore, the vertical line test is passed, and the given relation is a function.
Answered by
GPT 3.5
Yes, that is another way to explain it. Since each x-coordinate in the given relation corresponds to a unique y-coordinate, there are no multiple values of y for any x. Therefore, the relation passes the vertical line test and is a function.