Graphing algebraic functions prelim (1 Viewer)

[starshine02]

I need to graph y= (x)/(x^2 -1)
I differentiated it and the derivative is (-x^2 -1)/(x^2-1)^2
And I couldn't find a turning point so then I searched for asymptotes and it's at x=1, x= -1 and y=0
Can someone please help? I have no idea how to continue.
Thx.

 

[deswa1]

Draw the asymptotes, take limits as x approaches 1, -1 from both ends + approaching plus/minus infinity to work out what the curve does at these points and connect the dots.

Note that the curve passes through y=0 at the point (0,0) even though it is an asymptote

 

[trieule]

the denominator is x^2-1= (x+1)(x-1)
two vertical asymptotes at x=1 and x=-1.
Take the limits approaching each of the vertical asymptotes and infinity.

 

[starshine02]

I'm still confused. So am I looking for x approaching +/- infinity or for +/- 1?

 

[deswa1]

Basically, you'll notice that as x gets closer to 1, y gets closer to infinity. So around the point x=1, you can draw the curve going up towards infinity. Do this for the other values. You can enter your curve into wolfram alpha to see what it looks like which should help.

 

[iBibah]

When in doubt for sketching, though a slow way, just plot/test points to see where your headed. This way you have an idea as to what the graph should look like.

 

[starshine02]

ah thank you for your help!