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?

A) No, because the y-axis is a horizontal line.

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

C) Yes, because multiple y-intercepts represent multiple x-values being mapped to y = 0.

D) Yes, because the y-axis represents all vertical lines of the x-values.

Answer 1

I believe it’s b because this is not an accurate way of used the vertical line test. It only applies to the y intercepts, yet in another area an x coordinate could be with more than one y coordinate

Answer 2

Option B is the right answer.

Explanation:

To check whether a graph of a relation is a function or not we can use vertical line test.

The vertical line test for a function says that at any point on its domain, the vertical line through that point must intersect the curve only once. Even is there is one exception to this rule, the graph cannot represent a function.

Keeping this in mind, we can say what Shayla is doing is a wrong method as she test for vertical test only at a particular value of x=0 and not throughout the domain.

Hence option B is right

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