One of the functions is one to one , and the other is not.
Which function below is 1 to 1?
Function #2 on the right side is the one to one function . In a one to one function, every element in the range corresponds with one and only one element in the domain.
Only one thing must be true : each element in domain must go to a unique range element. ( prior lesson)
Diagram 2
To be a 1 to 1 function
Two things must be true.
First: It must be a standard function. In other words, it must satisfy requirements for
function .
Second: This is the new part. each element in range must go to a unique element in the domain.
Diagram 3
So, there is one new characteristic that must be true for a function to be one to one. This new requirement can also be seen graphically when we plot functions, something we will look at below with the horizontal line test.
Horizontal Line Test
We can also look at the graphs of functions and use the horizontal line test to determine whether or not a function is one to one.