HELP PLEASE ASAP Nora said: "Both Graph A and Graph B are functions because the y-axis intersects with each graph only once."

Janice said: "Neither graph is a function because Graph A has x values that repeat with different y values and Graph B has y values repeat with different x values."

Determine if either student is correct and explain, using appropriate math vocabulary, why you agree or disagree with each student.

Graph A is not a function

Graph B is a function

Explanation:

Graph A is not a function because it fails the vertical line test. We can draw a single straight vertical line through more than one point on the red graph. Eg: draw a vertical line through 5 on the x axis; it intersects the red graph at 2 locations.

Put another way, graph A shows that some inputs x lead to multiple outputs. A function is only possible when each input leads to exactly one output.

Graph B is a function because of this. It passes the vertical line test. It's impossible to draw a single straight vertical line to have it pass through more than one point on the blue graph.

Nora said both were functions while Janice said both are not functions. So both students are incorrect.

Nora's statement that "the y-axis intersects with each graph only once" is true, but there's more to the story as explained in the first paragraph above.

Janice seems to be mixing up the vertical and horizontal line tests. If she said that graph B wasn't one-to-one, then she would be correct due to the reasoning that "Graph B has y values repeat with different x values"; however, this fact does not lead to graph B not as a function.

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