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#1
02-12-2011, 03:28 AM
 chessimprov Novice Join Date: Sep 2009 Posts: 88 Somewhere else, US Math
Math question: 1-1 functions (vertical line test)

How does one use the idea of 1-1 for mathematical functions, in real life? Thank you.

#2
02-12-2011, 05:29 AM
 mopar Multitudinous Join Date: Aug 2010 Posts: 10,977 USA Kindergarten Teacher
I usually teach functions with getting paid for an hourly job. When you work one hour, you get x dollars. Then 2 hours, you should get 2x dollars, etc.

I guess, then you could say that the graph of the money you could make would be a function. You would get one amount of money each time you work....
#3
02-19-2011, 08:41 PM
 math1abee Companion Join Date: Feb 2011 Posts: 200 Georgia 7th Grade Math
Tying into mopar's idea of using it as a model for pay I always like to use attorney's as examples. If an attorney took your case you would pay him hourly. Then plug in how many hours they had to work on your case. It's also easy to form an equation using this example as well.
#4
02-19-2011, 09:00 PM
 mmswm Moderator Join Date: Nov 2007 Posts: 6,190 The land of fun and sun Former math teacher
Basic example from marketing....

A company makes widgets and sells them direct to the consumer. As it turns out, the widgets are popular, and demand is high. The company raises the price of the widgets since demand is so high (they want to make the most money, right?). These widgets are amazing! Demand is still high. The company raises the price again and people continue to buy the widgets at the even higher price.

At some point, widgets will reach a threshold where consumers will refuse to pay any more. Demand will go down. If the company continues to increase the price, demand will continue to go down. If you're picturing this correctly, you're seeing an downward opening parabola, who's vertex represents the maximum profit (y-coordinate) and the corresponding price the company can charge to generate the highest profit (x-coordinate).

A parabola, of course, is the graph of a quadratic function, which is not one-to-one.
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#5
02-20-2011, 08:14 AM
 HMM Habitué Join Date: Dec 2004 Posts: 828 OH Mathematics Professor
Quote:
 Originally Posted by mmswm A parabola, of course, is the graph of a quadratic function, which is one-to-one.

Quadratic function are not 1-1 unless you restrict the domain. They don't pass the horizontal line test.
#6
02-20-2011, 08:16 AM
 mmswm Moderator Join Date: Nov 2007 Posts: 6,190 The land of fun and sun Former math teacher
Quote:
 Originally Posted by HMM Quadratic function are not 1-1 unless you restrict the domain. They don't pass the horizontal line test.
I mistyped....I meant to say "not" one to one, but it does pass the vertical line test.
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#7
02-20-2011, 08:31 AM
 HMM Habitué Join Date: Dec 2004 Posts: 828 OH Mathematics Professor
Quote:
 Originally Posted by chessimprov How does one use the idea of 1-1 for mathematical functions, in real life? Thank you.
Quote:
 Originally Posted by mmswm I mistyped....I meant to say "not" one to one, but it does pass the vertical line test.
Then I guess I'm confused why you gave an example of a function that was not 1-1 since the OP was about examples that uses the Idea of 1-1?

I'm suspecting that the (vertical line) comment in the original subject is a misprint and should read horizontal line.

As for an example, I think mopar's is nice.
#8
02-21-2011, 05:20 PM
 Aliceacc Multitudinous Join Date: Apr 2006 Posts: 26,837 NEW YORK Math teacher
It's really two classifications: 1:1 and functions.

Functions have only one y for each x value. So, for example, each of the kids in my family has only one mom and only one dad. (We're not counting, for the sake of this example, Brian's birth parents.) The vertical line test is the standard way a kid can tell from a graph whether or not it's a function. Though, to tell you the truth, I think it oversimplifies things; the kids aren't remembering WHY it works, just testing for that vertical line.

Functions which are 1:1 add the requirement that each y also has only one x value. Kind of like one husband for each wife, and one wife for each husband.

Think of the ads for dating services: there are some that match you up with the one person they think will be perfect (1:1) and some that give you a list of possibliities (from your point of view, a function. Unless, of course, you're also one of several names they also give to someone else.)

As far as actually using them "in the real world"-- I would say that most people don't really use them. The definitions are ways we classify equations and relations in order to make studying them easier.

 Tags functions, line, math, question, test, vertical

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