Graphs: help! (2 Viewers)

Alkanes · Nov 27, 2011

big crocodile said:
Here, I would do an extremely simple question to depict my problematic problem

$y=\frac{1-x^{2}}{1+x^{2}} \\ D:\left \{ x \in \mathbb{R}\right \} \therefore \ $no vertical asymptotes$ \\\\\lim_{x \rightarrow \pm \infty }y= \lim_{x \rightarrow \pm \infty }\frac{\frac{1}{x^{_{2}}}-1}{\frac{1}{x^{2}}+1}=-1 \therefore \ y=-1 $is horizontal asymptote$ \\ \\f(-x)=f(x) \therefore y \, $is an even function$ \\ \\ y'=\dfrac{(1-x^{2})'(1+x^{2})-(1-x^{2})(1-x^2)'}{(1+x^{2})^{2}}=\dfrac{-4x}{(1+x^{2})^{2}}\\y''=\dfrac{12x^{2}-4}{(1+x^{2})^{3}} \\ \\ $Stationary points$: y'=0 \Leftrightarrow x=0; f(0)=-4\\\therefore (0,1)$is maximum point$ \\ $POI$: y''=0 \Leftrightarrow x=\pm \dfrac{1}{\sqrt{3}}\\ f(-2)=+;f(0)=-;f(2)+ \\ \therefore (\dfrac{-1}{\sqrt{3}},\frac{1}{2})\, $and$ \,(\frac{1}{\sqrt3},\frac{1}{2})\,$are the points of inflexion$$

okay, this is EXACTLY the 3 units method which is really time consuming. Also when I find the horizontal asymptotes, I cant figure it out right away. How would you do that?
And whenever I try to use to 4 units method, all my attempts are fail. For example in this question, after finding the asymptotes and 2 function $g(x)=1-x^{2}$ and $h(x)=1+x^{2}$ I have no idea how to make division between them:

yo guys have any idea to help me out? thanks

Graph looks neat. What program/software did you use?

big crocodile · Nov 28, 2011

SpiralFlex said:
For your division problem,

It is not a good idea to do so, but if you really want...and have lots of spare time.

$f(x)=1-x^2, g(x)=1+x^2$

$f(x)*\frac{1}{g(x)}$

this is my problem, i cannot add/subtract/multiply and divide functions, I always have to do the 3units method

big crocodile · Nov 28, 2011

Alkanes said:
Graph looks neat. What program/software did you use?

Geogebra. Its a free software which you can download from the internet: http://www.geogebra.org/cms/

Shadowdude · Nov 28, 2011

big crocodile said:
this is my problem, i cannot add/subtract/multiply and divide functions, I always have to do the 3units method

Start learning then, or you're going to be wasting loads of time on very easy marks.

big crocodile · Nov 30, 2011

yesh im really trying now. Im doing all kind of excercises from different textbooks. i think im overewhelmed -..-

SpiralFlex · Nov 30, 2011

Do not forget past paper questions...

big crocodile · Dec 10, 2011

uhmn.. I just wanna report, ive just got back my paper for ext2, 68% or sth. The weird part is I only got 11/20 for complex number and 16/20 for graphs.

lolcakes52 · Dec 11, 2011

a really easy thing to do which sound stupid is to find the vertical asymptote's, if there are any, and then plot one or two points on either side. This does not take long and will help you to understand what happens at certain times. 1-X^2/(1+x^2) for instance obviously is an even function, has a y intercept of 1 and x intercepts at plus and minus one. Finally, I have a hunch that the line will approach y=-1 as x tends to plus and minus infinity considering how 1-x^2 and 1+x^2 only have a difference of 2. People seem to not realise what they are looking at when they are asked a question and instead just start differentiating or something.

But if your finding maths hard then maybe you should consider dropping it, it may not be worth stressing over and you will pull the average mark down.

Graphs: help! (2 Viewers)

Alkanes

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big crocodile

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big crocodile

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Shadowdude

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big crocodile

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SpiralFlex

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big crocodile

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lolcakes52

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