Question

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?
○ no, because the y-axis is a horizontal line.
○ no, because using the y-axis tests only whether x = 0 is mapped to multiple values.
○ yes, because multiple y-intercepts represent multiple x-values being mapped to y = 0.
○ yes, because the y-axis represents all vertical lines of the x-values.

Explanation:

The vertical line test requires checking all vertical lines (not just the y - axis) to see if any vertical line intersects the graph more than once. The y - axis is \(x = 0\), so using only the y - axis to test for a function only checks if \(x=0\) is mapped to multiple \(y\) - values. It does not check for other \(x\) - values. Option 1 is wrong as the y - axis is vertical. Option 3 is wrong because multiple y - intercepts would mean \(x = 0\) is mapped to multiple \(y\) - values, but the vertical line test is about all \(x\) - values. Option 4 is wrong as the y - axis is just one vertical line (\(x = 0\)), not all vertical lines. So the correct option is the second one.

Answer:

No, because using the y - axis tests only whether \(x = 0\) is mapped to multiple values.