Graphing Functions Exercises

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Nyet (no). We can draw a vertical line and have it hit the graph in 3 places. That's overkill, since we should have had our answer the moment we hit the graph a second time, but no harm, no foul.

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Yes, this is a function. Any vertical line we draw will hit no more than one of the points in the relation. Even those two who are trying to hide along one of the axes. We see ya, fellas. Nice try.

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This is a function. Any vertical line will hit the graph no more than once. And some will fall right between the two segments of the graph. Missed it by that much.

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No, this is not a function. If we draw a vertical line through x = 2, we'll hit two different y-values. Only one little rule, graph, and you couldn't follow it? Man...you don't deserve to be a function.

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Nope, this isn't a function. There's a place where we can draw a vertical line and hit two different y-values. Just because part of this graph is a line and part of it appears in the form of a point doesn't get it off the hook. In fact, we're doubly upset with it for trying to be sneaky.

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This graph is a vertical line through x = 2:

Since a vertical line drawn through x = 2 hits every point in this infinite relation, the relation is not a function. In fact, it couldn't be less of a function if it tried. It's almost as if someone told him he should be a function, and he's acting out in utter defiance. Or maybe we're attributing too many human emotions and behaviors to non-thinking entities. It's been known to happen.

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Any vertical line will hit the graph no more than once. This relation is a function. It's lucky we're not performing the diagonal line test.

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If we draw a vertical line at any positive integer, we'll hit more than one point in the relation. This relation has a serious point infestation problem, and is clearly not a function.

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If we draw a vertical line at any positive integer, we will hit only one point in the relation. This relation is a function.

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This graph is a horizontal line through y = 3:

Since a vertical line will hit this relation only once, it is indeed a function. In the world of functions, horizontal lines are our friends. We might even ask them to sign our yearbook.