Question

If a graph passes the horizontal line test, but not the vertical line test, is it still a function?

Answer 1

If a graph fails the vertical line test it's not a function; you can't have a single x map to two ys.

Vice versa, if the graph passes the verticle line test, it's a function.  

The horizontal line test tests for injectivity aka one-to-one-ness; it has no bearing on whether something's a function.