Suppose a graph passes the horizontal line test: no horizontal line can be drawn that touches the graph in more than one location. does this mean that the graph represents a function? if not, is there anything special about a graph that passes the horizontal line test?

To check if an expression is indeed a function, you'd use the vertical line test, if it passes, then it IS a function.

now, if it passes the horizontal line test, doesn't mean much function wise, what the dickens is up with the horizontal line test anyway?

well, if the graph, does indeed pass the vertical line test first, is a function, IF then it also passes the horizontal line test, it means, is not only a function but a one-to-one function, meaning there's a unique x-coordinate value for every unique y-coordinate value.

note:

only one-to-one functions have an inverse expression that is also a function.

Multiplication property of zero

Where’s the