Question

to determine whether a graph is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times 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 she applying the vertical line test correctly

Answer 1

Answer:

Shayla is not applying the vertical line test correctly.

Step-by-step explanation:

The vertical line test is useful to determine whether the provided curve is a graph of function or not.

Vertical line test: If we draw a vertical line anywhere on xy plane and the vertical line intersect the graph more than once, then the graph is not a function.

Consider the figure 1:

The vertical lines intersect the graph exactly at one spot. it doesn't matter where we drop the vertical line.

Now consider the figure 2:

Here, the graph has exactly one y-intercept, but it doesn't follow the vertical line test as the graph hits the vertical line in two spots.

Therefore, she is not applying the vertical line test correctly.

Answer 2

Shayla is not applying the vertical line test correctly because it may be a specific function that only intersects the y-axis once but may intercept other values of x multiple times, in order to correctly apply the vertical line test to determine if a graph shows a function or not you must test for multiple points at all x-values of a graph.