Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x and y axes range from -6 to 6 in increments of 1. A semicircle is graphed on the plane. The semicircle passes through points plotted at coordinates (-5 , 0), (0 , 5), and (5 , 0).
The graph of a relation is given. Apply the vertical line test to determine if this relation is a function. Enter 1 if the relation is a function. Enter 2 if the relation is not a function.
2
it is a function
I apologize for the confusion. If the semicircle passes through points plotted at (-5, 0), (0, 5), and (5, 0), then it means that for each value of x (input), there is only one corresponding value of y (output). Therefore, the relation is a function. The answer is 1.
To apply the vertical line test to the graph of the given relation, we need to determine if there is any vertical line that intersects the graph in more than one point. If such a line exists, then the relation is not a function.
Looking at the graph, we see that the points plotted on the semicircle are symmetric around the y-axis. This means that for any value of y, there are two corresponding x-values on the semicircle.
Let's draw a vertical line that intersects the graph. If we draw a line at any x-value (except -5, 0, and 5 where the points are located), it will intersect the graph at exactly one point. However, if we draw a line at x = -5, x = 0, or x = 5, it will intersect the graph in two points (-5, 0) and (5, 0).
Since there exists at least one vertical line that intersects the graph in more than one point, we conclude that the relation is not a function.
Therefore, the answer is 2.