help with curve sketching 4u question (1 Viewer)

[greenlemings]

Hi im just a beginner at 4u and im having trouble with curve sketching. Can someone sketch y=(x^2)/ (x^2-1) and then sketch (x^2-4x+4)/(x^2-4x+3)? Also can i have like a detailed working out of it? Its a case of f(x) into f(x-a) but idk what the a is. Thanks everyone.

 

[Ambility]

I think this question is actually within the 3U syllabus.

First graph: http://i.imgur.com/bsxs98p.jpg

Second graph: http://i.imgur.com/LXFATpP.jpg

 

[greenlemings]

thanks but how do i sketch the second one

 

[Ambility]

I've added the second one into my post now.

 

[KingOfActing]

Here's how I would do them:



So the curve has the vertical asymptotes at , and tends to 1 both in the positive and negative direction. Looking at the equation, we get that the curve is positive when x > 1 or x < -1 and negative at -1< x < 1. Additionally, looking at the original form of the function, we can see that the only zero of the curve is x = 0 (alternatively, notice that it has a 'double root' at x = 0, so the curve won't change sign around that point). Graphing this (crudely with MS Paint because I'm lazy):



Now using this sketch:



Notice that the second curve is a translation to the right by 2 (x was replaced with x-2). Just redraw the same curve, two units to the right.

 

[Green Yoda]

I dont know if its unusual but we are doing these rational functions at the start of yr 11..one of the most fun topics currently for maths haha

 

[greenlemings]

thanks heaps!

 

[leehuan]

I dont know if its unusual but we are doing these rational functions at the start of yr 11..one of the most fun topics currently for maths haha

It's technically under the 2u topic of real functions as a 3u additional part, just like integration by substitution is a part of 2u integration