Functions - Domain and One-to-One, Onto

                     Lesson 1

 

one-to-one

Onto

 

 

A function f from A to B is called one-to-one (or 1-1) if whenever
 f (a) = f (b) then a = b.   No element of B is the image of more than one element in A.

A function f from A to B is called onto if for all b in B there is an a in A such that

f (a) = b.

All elements in B are used.

 

 

Domain

Range

 

 

The domain is the set of all first elements of ordered pairs

(X-coordinates).

The range is the set of all second elements of ordered pairs (y-coordinates).

 

                                                                                                                                                                          

                                                           

                                                            Problem:   Find the domain of :{( 4, 5), (6,7),(8,9),(10,11)}

                                                            

                                                            Solution    The domain is the set of all first elements of ordered pairs = {4, 6, 8, 10}                 

                                                            Step 1:                                                                                                                                                             

                     

                                                            Solution    Domain: {4, 6, 8, 10}                 

                                                            Step 2:                            

                                                                                         

                                                            Solution    Answer is: {4, 6, 8, 10}                 

Step 3:                                                            

Complete                                                                   

                                                                                                                               

                                                             Try two practice problems:  

 

                                                                                Solve the following:    

A.

Find the domain of the function

f (x) = 2x2-2x+12

 

B.

Find the domain

 

of: {(9,10),(11,12),(13,14),(15,16)}

 

2

 

 

 

 

 

        

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