A graph is shaped like the letter 'C' (a parabola opening to the left). Does this graph represent a function?

Yes, because it is a single continuous curve.

No, because a vertical line can intersect it at two points.

Yes, because it crosses the y-axis.

No, because it does not pass through the origin.

What is the fundamental reason the vertical line test works for identifying functions?

It ensures every output `y` has a unique input `x`.

It confirms the graph is a straight line.

It ensures every input `x` has exactly one output `y`.

It checks if the graph has both positive and negative values.

A circle with its center at the origin.

A sideways parabola opening to the right.

An oval centered at the origin.