Discovering the Function f(x)=x+1/x | Expert Help & Thanks in Advance!

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SUMMARY

The function f(x) = x + 1/x is characterized by its limit approaching 1 as x approaches infinity and is undefined at x = 0. In China, it is referred to as the "nike curve." Graphing tools such as Graphmatica and Calc101 are recommended for visualizing this function, which is classified as an odd function exhibiting antisymmetry.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with odd functions and antisymmetry
  • Basic graphing skills using software tools
  • Knowledge of function notation and terminology
NEXT STEPS
  • Research the properties of odd functions and their graphs
  • Learn how to use Graphmatica for graphing functions
  • Explore the features of Calc101 for online graphing
  • Study the concept of limits in calculus, particularly at infinity
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Mathematics educators, students studying calculus, and anyone interested in graphing functions and understanding their properties.

sophiaqiu
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help! thanks in advance!

Homework Statement



what do you know about this function:f(x)=x+1/x

Homework Equations





The Attempt at a Solution

 
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uh... it's a function?

What do you want to do with it?
 
its limit is 1 when x->infinity
it is not defined when x=0

yeah like christian stated

what's your deal with it??
 
yes,I know,now I want to know how do you call it in your country,we call it "nike curve" in China,I want to know how do you teach your students in maths teaching?did you use the sketchpad to graph it??
 
I graphed it use Graphmatica, give that a search in google and its free.

You don't need to call it anything Sophia, just tell the students f(x)=x+1/x. That's all. And just incase you wanted some helpful info on actually graphing it, its an odd function so there's antisymmetry. and www.calc101.com has a graphing program on it, that might help as well.
 

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