Chapter 2 - Functions and Their Graphs - 2.2 The Graph of a Function - 2.2 Assess Your Understanding - Page 69: 51

The Vertical Line Test says that every vertical line drawn can only intersect the graph in at most one point for the graph to represent a function. Recall that a function has one $y$-value paired to every $x$-value.. Hence, if a graph fails the Vertical Line Test , that means there are at least $2$ $y$'s paired to the same $x$. Thus, the graph cannot possibly represent a a function.

The Vertical Line Test says that every vertical line drawn can only intersect the graph in at most one point for the graph to represent a function. Recall that a function has one $y$-value paired to every $x$-value.. Hence, if a graph fails the Vertical Line Test , that means there are at least $2$ $y$'s paired to the same $x$. Thus, the graph cannot possibly represent a a function.