What is a one to one function plus examples?

Answer 1

See the related link - Math Warehouse.

• First it has to be a function, that means for each and every x value, there is one and only one y value. Often the term vertical line test, is used. That means a vertical line will cross the graph only one time at every x value, then it is a function.
• If it is a function, and for every y-value, there is only one x-value, then it is a one-to-one function. Often you may see horizontal line test, as a way of checking.

Examples of one-to-one functions:

• y = x
• y = 2x +3
• y = e^x

Examples of functions, which are notone-to-one:

• y = x² [parabola: (2)² and (-2)² both equal 4]
• y = sin(x) [y will oscillate back and forth between +1 and -1 indefinitely]

If a function passes the tests and is a one-to-one, then the function will have an inverse.

Also, a function can be defined as one-to-one over a specific range. Like x² for all x > 0 {positive numbers}