The graph show a function A. Yes, the graph passes the vertical line test , C. Yes, there are no y values that have more than one x-value. Therefore, A. Yes, the graph passes the vertical line test ,C. Yes, there are no y values that have more than one x-value is correct.
To determine if a graph represents a function, we can employ the Vertical Line Test.
This test asserts that if any vertical line intersects the graph at most once, then the graph represents a function.
Option A, "Yes, the graph passes the vertical line test," aligns with the fundamental principle of the Vertical Line Test.
When any vertical line is drawn across the graph, it intersects the graph at most once, indicating a one-to-one correspondence between x-values and y-values.
This conformity to the Vertical Line Test is a strong indication that the graph indeed represents a function.
Similarly, option C, "Yes, there are no y values that have more than one x-value," reinforces the concept behind the Vertical Line Test.
If each y-value is associated with only one x-value, it ensures that there are no ambiguities or multiple mappings, reinforcing the idea that the graph represents a function.
In conclusion, both options A and C essentially express the same idea—that the graph adheres to the conditions of the Vertical Line Test, and as such, it represents a function.
The concurrence of these options emphasizes the reliability of the conclusion drawn from the Vertical Line Test.