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May 9th, 2016, 11:04 PM  #1 
Newbie Joined: Dec 2015 From: North America Posts: 20 Thanks: 2 Math Focus: my graphics calculator  recognizing onetoone functions
Dear math people, I am refreshing my brain cuz i'm planning to retake the equivalent of math 12 (precalc?) this summer before I go back to school and take math... can't remember ever studying this though... so right now I'm doing some selfstudy... I am supposed to: determine which of the given relations ins a onetoone function over its domain. {(1,a),(2,d),(3,b)}, {(1,b), (2,c),(3,b)}, {(1,a),(2,c),(3,b),(1,d)}, {(1,b),(1,c),(1,d),(2,a)}, {(1,d),(2,d),(3,d)} I'm supposed to pick one. I wasn't sure how to answer this so I checked the answers at the back of the book and according to the back the correct answer is... the back of the book stated that the correct answer is the very first set {(1,a),(2,d),(3,b)}, because there is only 1 x value to 1 y value and vice versa, but I'm not sure how they came to that conclusion from staring at a bunch of numbers/letters. As in, without graphing it out... so effectively the back of the book didn't 'show their work' so I don't know how they came to that conclusion. My math 12 is rusty, please forgive me, for those of you that read this, please care to explain? Please and thank you! 
May 10th, 2016, 12:48 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
Try to draw a diagram for each of these. Write down the domains and codomains in two separate columns, and line up the elements according to the binary relations. Then you'll see why. 
May 10th, 2016, 04:38 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416 
Let's go over a couple of the incorrect choices ... {(1,b), (2,c),(3,b)}, note the two function values, f(1) = f(3) = b, are the same value. onetoone functions have unique function values for every value in the domain {(1,a),(2,c),(3,b),(1,d)}, not a function ... 1 maps to both a and d Given the two explanations above ... {(1,b),(1,c),(1,d),(2,a)}, you tell me what's wrong with this choice {(1,d),(2,d),(3,d)}, you tell me what's wrong with this choice, also. 
May 10th, 2016, 04:19 PM  #4 
Newbie Joined: Dec 2015 From: North America Posts: 20 Thanks: 2 Math Focus: my graphics calculator 
ohh i think i'm starting to get it... {(1,b),(1,c),(1,d),(2,a)}  they are stating that the value of x has 3 different y values, (b c and d)... therefore it's not a onetoone function because a onetoone function has to have one x value to one y value and vice versa {(1,d),(2,d),(3,d)}  similar idea, for the y value of 'd', there are 3 x values (1 and 2 and 3) meaning that it is also not a onetoone function i think i understand this particular question now thank you 
May 10th, 2016, 04:21 PM  #5 
Newbie Joined: Dec 2015 From: North America Posts: 20 Thanks: 2 Math Focus: my graphics calculator  thanks for bearing with me!
lol it's been a long while since math 12

May 10th, 2016, 04:31 PM  #6  
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416  Quote:
 

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