|
One-to-One Function
|
One-to-One
|
|
A function  is one-to-one if distinct input values are mapped by  to distinct output values. A synonym for one-to-one 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 One-to-One 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 one-to-one).
If your function is one-to-one, you can draw its inverse by clicking Invert.
Clear an existing graph by clicking it.
|
|
Download Help Document
Was this information helpful?
