OnetoOne Function
OnetoOne

A function is onetoone if distinct input values are mapped by to distinct output values. A synonym for onetoone is injective.



In order for the function to be invertible, the problem of solving for must have a unique solution. This is because for the inverse to be a function, it must satisfy the property that for every input value in its domain there must be exactly one output value in its range; the inverse must satisfy the vertical line test. Since the domain of the inverse is the range of and the range of the inverse is the domain of , this means that in order for to be invertible, its graph must satisfy the horizontal line test: Each horizontal line through the graph of must intersect that graph exactly once.

Creating a OnetoOne Function


Click and drag with your mouse to draw a function in the plot below.
The horizontal line test is performed, and the title indicates whether the function you've drawn passes this test (so it is onetoone).
If your function is onetoone, you can draw its inverse by clicking Invert.
Clear an existing graph by clicking it.


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