anonymous
  • anonymous
how to sketch 1+ [2/(x+1)]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
u mean a graph?
anonymous
  • anonymous
r u der?
anonymous
  • anonymous
yes a graph

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anonymous
  • anonymous
alright, lets take the given function as y so, y=1+[2/(x+1)]
anonymous
  • anonymous
now, substitute x=0, u'll get y value, so this gives u one point on the graph like (x,y) i think u know how to plot point on a graph , right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
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anonymous
  • anonymous
thank you very much lokisan ^.^
anonymous
  • anonymous
you still need to do what thinker was doing...i.e. drawing it yourself
anonymous
  • anonymous
and yeah...try plugging more point..x=-1,1, -2,2,....so on..to get a good graph :)
anonymous
  • anonymous
sry *points
anonymous
  • anonymous
and the graph that u get finally is a symmetric one, i.e. symmetric about the 1st & 3rd quadrants
anonymous
  • anonymous
This one shows both asymptotes.
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anonymous
  • anonymous
thank you very much thinker! =]
anonymous
  • anonymous
You should notice some qualitative aspects of the function to make your drawing easier. For example, as x approaches -1, the function approach plus or minus infinity, depending on which direction -1 is being approached. As x goes to plus or minus infinity, the function goes to 1.
anonymous
  • anonymous
ur welcome @virtus :)
anonymous
  • anonymous
i'm a bit confused on the asymptotes bit i know we can determine one asymptote by looking at the denominator of the fraction but how did you get the other, y =1
anonymous
  • anonymous
Once you get a bit more advanced, you'll notice that your function is just a composition of functions and that what you've got is just a hyperbolic function (1/x) that has been translated by a horizontal shift (i.e. x goes to x+constant)) with the result of that multiplied by 2 (thereby pushing the corner of the hyperbola further out) and then the entire thing shifted up 1 unit.
anonymous
  • anonymous
\[y=1+\frac{2}{x+1}\]What happens as x gets larger without bound?
anonymous
  • anonymous
Very large positive x will make 2/(x+1) a very small positive number. Very large negative x will make 2/(x+1) a very small negative number. You'll be adding/subtracting very small amounts for large x. As x gets large, this effect is more pronounced.
anonymous
  • anonymous
So basically, the function approaches the value 1 and x approached plus or minus infinity.
anonymous
  • anonymous
You can see that in the plot.
anonymous
  • anonymous
Btw, the software I used to make that plot is free: http://www.geogebra.org/cms/
anonymous
  • anonymous
got it @virtus?
anonymous
  • anonymous
oh well, we'll assume virtus has got it... :p
anonymous
  • anonymous
hahahhas sorry for late reply THANK YOU SO SO MUCH!
anonymous
  • anonymous
np
anonymous
  • anonymous
ur wc
anonymous
  • anonymous
Use wolframalpha http://www.wolframalpha.com just write your formula and hit Enter

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