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.
To determine whether 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 a graph at more than one point, then the graph does not represent a function. On the other hand, if every vertical line crosses the graph at most once, then the graph represents a function.
So, let's plot the given points on a graph:
-6 | .
|
-5 |
|
-4 |
|
-3 |
|
-2 | .
| .
-1 |
|
0 | .
|
1 |
|
2 |
|
3 | .
| .
From the plotted points, we can see that for every vertical line we draw, it only intersects the graph at most once. There are no vertical lines that intersect more than one point on the graph.
Therefore, since no vertical line crosses the graph more than once, the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} satisfies the vertical line test, and it represents a function.