Question

Noemi says that a graph of an oval is a function

because she can trace the whole graph without
picking up her pencil. Mark says that an ovál is
not a function because multiple values of x map to
the same y-value. Determine if either one is
correct and justify your answer completely.

Answer 1

Noemi is wrong with wrong justification.

Mark is correct but his justification is incorrect.

Explanation:

Given:

A graph of oval shape.

The reason given by Noemi to call it a function is because she can draw it without lifting her hand.

The reason given by Mark to reject it as a function is because multiple values of 'x' map to same value of 'y'.

A function is said to be defined only if each 'x' value has unique 'y' value. In other words, no two values of 'y' can have the same 'x' value. Therefore, multiple values of 'x' can map to same values of 'y' but multiple values of 'y' can never map to same values of 'x'.

So, here, the reason given by Noemi is not for a function but for a definition of continuous function.

The reason given by Mark is also not correct as multiple values of 'x' can map to same values of 'y' but the converse is not true.

So, the graph of a oval shape is not a function as multiple values of 'y' maps to same value of 'x'