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 if the relation is a function, we need to use the vertical line test. According to the vertical line test, a relation is a function if no vertical line intersects the graph of the relation more than once.
Here, let's plot the given points on a graph:
(-6, -2) |
(-2, 6) |
(0, 3) |
(3, 5) |
Now, let's draw a series of vertical lines through the graph:
|
|
|
|
-6|
-5|
-4|
-3|
-2|______|______|___•
-1| \
0|____•__________\__________•
1| /
2|______|______/___________
3|______|______|
As we can see, no vertical line intersects the graph more than once. Hence, the vertical line test confirms that the relation is a function.
Therefore, the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function.