One-to-one Functions

Definition:
A function f, is one-to-one if, for a and b in its domain,
               f(a) = f (b) implies that a = b 

1. Each y- coordinate will only have one x- coordinate
2. The graph of the function must pass the horizontal line test


ex.                                   
                       step one: set the two functions equal to each other
                                            - 1                   -1         step two: subtract 1 from both sides 


                         
                                     step three: square both sides
                                           a = b
                      therefore f (a) = f (b) which implies that a = b so it is a one-to-one function

ex.                  
                          step one: set both functions equal to each other
                               step two: divide both sides by 3
                          
                                      + 1                         +1                   step three: add 1 to both sides 
                                          
                                                  step 4: take the square root of both sides 
                                                            Since you are left with two options for b this is not a one-to-one function. 
                                                                                     One-to-one functions can only have one solution for each.

-Amanda