One To One Function

This page contains the separate images from the One-to-one Function video.

This is an example of a one-to-one function.

Notice that for any certain x-value....

there is only one y-value.

So, one x (the input) matches with one y (the output). That is why this is called a one-to-one function.

Here is another x-value.

It, too, matches with only one y-value.

Notice that any vertical line that you draw will intersect the graph only once. This is proof that the graph represents a function. We say that this graph has passed the vertical line test.

Here is another one-to-one function. One-to-one functions can appear as either a straight or curved line.

Again, one x-value (the input) matches up with only one y-value (the output).

And, again, any vertical line intersects the graph only once. The graph passes the vertical line test, and this proves that the graph represents a function.