Staring at a graph and wondering, "Which relation graphed below is a function?" Don't sweat it! Identifying functions from their graphs is easier than you think. The secret weapon? The Vertical Line Test.
Imagine drawing vertical lines through your graph. If *any* vertical line intersects the graph more than once, it's NOT a function. Why? Because a function, by definition, can only have one output (y-value) for each input (x-value). A vertical line hitting the graph twice means that particular x-value has two different y-values – a no-no for functions!
So, next time you're faced with a collection of graphs, channel your inner artist and start drawing those imaginary vertical lines. If every single one passes the test (intersecting the graph only once), congratulations, you've found a function! If even one fails, move on; it's not a function.
