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May 10th, 2017, 07:40 AM  #1 
Newbie Joined: May 2017 From: far away Posts: 2 Thanks: 0  on Vertical line test and definition of a function
Vertical line test “A function can only have one output, y, for each unique input, x.” – from Wikipedia Why do we want a function to have only one output? 
May 10th, 2017, 08:25 AM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,607 Thanks: 819 
by definition a function evaluated at a point must have only one result. function mappings cannot be one to many 
May 10th, 2017, 10:06 AM  #3 
Senior Member Joined: Feb 2010 Posts: 632 Thanks: 103  Imagine you owned a vending machine company. How happy would you be if every time a customer input $1.50 they got out two bottles of water rather than one? You are sitting on your couch at home. You grab the remote control. You input channel 49. How happy would you be if you got ESPN and PBS simultaneously broadcast on top of one another? If these things happened, then your vending machine and your remote control would not be FUNCTIONing properly. 
May 12th, 2017, 05:06 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,829 Thanks: 753 
This is related to the basic science idea of "repeatable" results if you do the same experiment with exactly the same conditions, you should get the same result. That is the result of the experiment is a function of the initial conditions.

May 12th, 2017, 05:58 AM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,042 Thanks: 2344 Math Focus: Mainly analysis and algebra  For me, there are two main reasons:

May 13th, 2017, 06:05 PM  #6 
Newbie Joined: May 2017 From: far away Posts: 2 Thanks: 0 
Thank you for your great replies, I really appreciate it.

May 13th, 2017, 10:53 PM  #7 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 
Imagine you get into bed with your girlfriend. How happy would you be if she brought her smoking hot sister? 
May 13th, 2017, 11:11 PM  #8 
Senior Member Joined: Aug 2012 Posts: 1,641 Thanks: 415  

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definition, function, line, test, vertical, vertical line test 
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