I need help understanding domain and range. For example. The time it takes to bicycle m miles at a rate of 15 miles per hour.

Question

MY teacher tried to explain it to me a little bit....I still don't understand.  Like HOW???

Answer 1

Dear Natalya,

     Domain is a set of "X" values, and "Y" is a set of Y values, which are usually dependent on what the "X" value is.

 

For example,  Y=2X  .  Let's look at a table for this problem.  All we have to do is make up a few values for X and see how these values change "Y":

 

                                                     X                 2X            Y  

                                                     0                2(0)         0

 

                                                     1                2(1)         2

                                    

                                                     2                2(2)         4

 

                                                     3                2(3)         6

                                      

                                                    4                 2(4)         8

 

Domain:   {0,1,2,3,4,...}                              Range: { 0,2,4,6,8,...}

 

What is the relationship of Y to X?    _______________

 "Y" is twice the value of "X."

 

Now, let's look at the problem that you presented.  I will also place it in a table.  Here is an equation related to time, distance, and rate:     Rate * Time= distance.   Let "t=time in hours and m=distance

 

Let t=X     and Y=m    Then suppose you want the domain and range of this problem:

 

 

                                                            Rate        *        Time    =                    Distance

 

                                                             15 mi/h             t=X             15*t   =    m=Y

 

                                                          15                         1 hour   =15*1=            15

 

                                                          15                         2 hours  =15*2=            30

 

                                                          15                         3 hours  =15*3=            45

 

                                                          15                        4 hours=15*4=               60 

 

 

 

Note:  The distance you travel is related to the number of hours you drive.

 

Domain:     t=X={1,2,3,4,...}             Range:  m=Y={15,30,45, 60,...} 

 

The three dots indicate that you could keep substituting time values and come up with more values for the range in miles.

 

If you have further questions, just feel free to ask.  Also, if I have helped you, please give me a thumbs up.

 

                                                                             Susan C.