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?

Answer 1

Shayla's use of the vertical line test is incorrect because she is only considering the number of y-intercepts, which is not conclusive in determining if a graph is a function. The correct method is to see if any vertical line intersects the graph at more than one point.

Step-by-step explanation:

Shayla is not applying the vertical line test correctly. The correct use of the test involves drawing vertical lines through various points on the graph and checking to see if any vertical line intersects the graph at more than one point. A graph represents a function if, and only if, every vertical line intersects the graph at most once. The number of y-intercepts, or where the graph intersects the y-axis, is not a reliable indicator of whether a graph is a function. For example, a straight line with a slope and a y-intercept, such as in the form y = mx + b, will always be a function, regardless of the number of y-intercepts it has.

Answer 2

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