Question
Six graphs are shown below. Graph 2 is a diamond centered at the origin, with vertices at approximately $(0,2)$, $(2,0)$, $(0,-2)$, and $(-2,0)$.Does Graph 2 represent a function? Use the vertical line test and explain your answer.
Answer
No. Graph 2 does not represent as a function of .
Draw the vertical line . It meets the diamond at both and . Thus the single input would have two output values.
Because at least one vertical line intersects the graph more than once, Graph 2 fails the vertical line test.
Evidence boundary
This answer covers only Graph 2, the diamond that is fully visible in the cited prompt. The four vertex coordinates are read from the displayed coordinate grid and are approximate, but the conclusion does not depend on their exact scale: a vertical line through the diamond intersects it twice. The other five tabbed graphs are not visible in the source and are not answered here.
Sources
These references support the concepts and methods used in the explanation above.