How does the vertical line test identify a function?

"You might also remember discussing functions in high school math, and the so-called “vertical line test.” When you plotted the values of a numerical function on a graph, and there was no vertical (up-and-down) line that intersected more than one point, you could safely call the plot a “function.” That’s really exactly the same thing as the condition I just gave for functions, stated graphically. If a plot passes the vertical line test, then there is no x value for which there’s more than one y value. This means it makes sense to ask “which is the value of y for a particular value of x?” You’ll always get one and only one answer. There’s no such thing, of course, as a “horizontal line test,” since functions are free to map more than one x value to the same y value. They just can’t do the reverse. The difference between the functions of high school math and the functions we’re talking about here is simply that our functions aren’t necessarily numeric. Sometimes we do draw “plots” of sorts, though, like this one: Harry, Ron, Hermione, Mt. Dew, Dr. Pepper. This simply shows which elements of the domain map to which elements of the codomain. The left blob is the domain, the right blob is the codomain, and there’s an arrow representing each mapping."