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Mathematics 18 Online
OpenStudy (anonymous):

how to sketch 1+ [2/(x+1)]

OpenStudy (anonymous):

u mean a graph?

OpenStudy (anonymous):

r u der?

OpenStudy (anonymous):

yes a graph

OpenStudy (anonymous):

alright, lets take the given function as y so, y=1+[2/(x+1)]

OpenStudy (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?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

OpenStudy (anonymous):

thank you very much lokisan ^.^

OpenStudy (anonymous):

you still need to do what thinker was doing...i.e. drawing it yourself

OpenStudy (anonymous):

and yeah...try plugging more point..x=-1,1, -2,2,....so on..to get a good graph :)

OpenStudy (anonymous):

sry *points

OpenStudy (anonymous):

and the graph that u get finally is a symmetric one, i.e. symmetric about the 1st & 3rd quadrants

OpenStudy (anonymous):

This one shows both asymptotes.

OpenStudy (anonymous):

thank you very much thinker! =]

OpenStudy (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.

OpenStudy (anonymous):

ur welcome @virtus :)

OpenStudy (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

OpenStudy (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.

OpenStudy (anonymous):

\[y=1+\frac{2}{x+1}\]What happens as x gets larger without bound?

OpenStudy (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.

OpenStudy (anonymous):

So basically, the function approaches the value 1 and x approached plus or minus infinity.

OpenStudy (anonymous):

You can see that in the plot.

OpenStudy (anonymous):

Btw, the software I used to make that plot is free: http://www.geogebra.org/cms/

OpenStudy (anonymous):

got it @virtus?

OpenStudy (anonymous):

oh well, we'll assume virtus has got it... :p

OpenStudy (anonymous):

hahahhas sorry for late reply THANK YOU SO SO MUCH!

OpenStudy (anonymous):

np

OpenStudy (anonymous):

ur wc

OpenStudy (anonymous):

Use wolframalpha http://www.wolframalpha.com just write your formula and hit Enter

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