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Determine if the following graph shows a function.

Time for the good old reliable vertical line test. We can draw a vertical line through the graph and have the line hit the graph more than once:

Because our vertical line hits the graph more than once, there's an x-value getting matched with more than one y-value. Scandal! Sadly, this is not the graph of a function.

Example 2

Determine if the following graph shows a function.

No matter where we draw a vertical line, we will hit the graph no more than once:

That means this is the graph of a function. Thank goodness! This news should be enough to get us out of our func.

Example 3

Determine if the following graph shows a function.

Yes, the graph shows a function. Although it is a bit "all over the place" and doesn't seem to be sure of where it wants to go, a graph does not get penalized for indecision. Any vertical line we draw will hit the graph at most once, and might not hit the graph at all, which is totally okay, and that is all we care about. Oh, and also the environment.