Question

Is the following relation a function?

Circle centered at the origin with radius 1.

a) Yes
b) No

Answer 1

No, the relation is not a function because there are multiple outputs for each input.

Step-by-step explanation:

No

A relation is only considered a function if each input has exactly one output. In the case of a circle centered at the origin with radius 1, there are multiple outputs (y-values) for each input (x-value). Therefore, this relation is not a function.

For example, if we consider the points on the circle at the coordinates (1, 0) and (-1, 0), both points have the same x-coordinate (input), but different y-coordinates (outputs).