To determine whether a graph of a relation is also a function, Shayla declares that the y -axis is a vertical line and counts the number of times that the graph intersects the y -axis. If the graph has exactly one y -intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function. Is Shayla applying the vertical line test correctly?
Answer
A
Yes, because multiple y -intercepts represent multiple x -values being mapped to y is equal to 0 .
B
Yes, because the y -axis represents all vertical lines of the x -values.
C
No, because the y -axis is a horizontal line.
D
No, because using the y -axis tests only whether x is equal to 0 is mapped to multiple values.
Explanation
The vertical line test checks whether any vertical line intersects the graph more than once. The y-axis is only the vertical line x = 0, so checking it tests whether x = 0 is paired with multiple y-values; it does not test the rest of the graph. Shayla could miss a vertical line elsewhere that intersects the graph multiple times, so the correct choice is “No, because using the y-axis tests only whether x is equal to 0 is mapped to multiple values.”
AI-written and checked against the verified answer.