Which simple graphical procedure determines whether a curve $y=g\left(x\right)$ represents a function of $x$?

Use the horizontal line test: if every horizontal line intersects at least once, it's a function

Check whether the graph passes through the origin; it is a function only if it does

Use the vertical line test: if every vertical line intersects the graph at most once, it's a function

Count the number of peaks and troughs; only functions with fewer than two peaks are included