The vertical line test is a test to determine whether or not a relation is a function.

If a vertical line can be drawn anywhere in the coordinate plane so that it intersects the graph of a relation at more than one location, then the relation is NOT a function.

If a vertical line is drawn anywhere in the coordinate plane and intersects the graph of a relation at zero locations or one location, the relation IS a function.

The relation g: y = x² - 2x - 3 IS a function, since a vertical line intersects the graph of the relation at exactly one location, regardless of where the vertical line is drawn.

Since relation g is a function, it can be written using function notation as g(x) = x² - 2x - 3.

The relation S: x = y² IS NOT a function, since a vertical line can be drawn that intersects the graph of the relation at more than one location.

Since relation S is NOT a function, it should NOT be written using function notation.