While performing a vertical line test, you notice that the graph intercepts the vertical line twice. Which of the following correctly interprets the result of the test?
The graph is a relation, but is not a function.
The graph is both a relation and a function.
The graph is a neither a function or a relation.
The graph is a function but is not a relation.
The correct answer is: The graph is a relation, but is not a function.
The correct interpretation of the result of the vertical line test, when the graph intercepts the vertical line twice, is that the graph is a relation, but is not a function.
To interpret the result of the vertical line test, we need to understand the concept of a function and a relation.
A relation is a set of ordered pairs that relate two sets of values. In other words, it is a collection of points in a coordinate system.
A function is a special type of relation where each input value (x-value) is associated with only one output value (y-value). In other words, for every x-value, there is a unique y-value.
Now, let's apply the vertical line test. The vertical line test is a method used to determine if a graph represents a function. To perform the test, imagine moving a vertical line from left to right across the graph.
If the vertical line intersects the graph in at most one point for every x-value, then the graph represents a function. This means that each x-value has a unique y-value.
However, if the vertical line intersects the graph more than once for any particular x-value, then the graph does not represent a function. This implies that there exists an x-value with multiple corresponding y-values.
In the given scenario, since the graph intercepts the vertical line twice, this means that there is at least one x-value with two corresponding y-values. Therefore, the correct interpretation of the result is:
The graph is a relation, but is not a function.
Option 1: "The graph is a relation but is not a function" is the correct answer.