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 to determine if a graph represents a function. According to this test, if you can draw a vertical line that intersects the graph in more than one point, then the graph does not represent a function. This is because in a function, each input (or x-value) must correspond to exactly one output (or y-value).
Given the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)}, we don't have the graph, but we can analyze the set of ordered pairs to see if it satisfies the definition of a function. We have to check if each x-value (the first number in each pair), which represents the input, is associated with only one y-value (the second number in each pair), the output.
In the given set of ordered pairs:
- The x-value –6 corresponds to the y-value –2.
- The x-value –2 corresponds to the y-value 6.
- The x-value 0 corresponds to the y-value 3.
- The x-value 3 corresponds to the y-value 5.
All the x-values are unique, and each x-value is paired with only one y-value. There are no repeating x-values with different y-values, which means that no vertical line would intersect the graph at more than one point.
Thus, based on the vertical line test and the definition of a function, the given relation is a function because each input has a unique output.