# Sketching x/x+2

• Feb 15th 2011, 06:34 PM
gbenguse78
Sketching x/x+2
Hi
I am trying to understand how to sketch the above named graph. I have obtained the vertical asymptote as x = -2 but not sure of the horizontal asymptote. Examining the graph as x tends to infinty, it seems the horizontal asymptote is 1. But I am stuck at this stage. Any help or suggestions? I am not sure of the shape of the graph also. Thanks.(Worried)
• Feb 15th 2011, 06:48 PM
Prove It
It would help if you rewrote this as $\displaystyle \frac{x}{x+2} = \frac{x+2-2}{x+2} = 1 - \frac{2}{x+2}$.
• Feb 15th 2011, 07:34 PM
gbenguse78
Quote:

Originally Posted by Prove It
It would help if you rewrote this as $\displaystyle \frac{x}{x+2} = \frac{x+2-2}{x+2} = 1 - \frac{2}{x+2}$.

I tried that and the graph is the form 1/x. There will be a horizontal translation of 2 units to the left (Vertical Asymptote). It seems the graph will be reflected in the y axis and a vertical translation of 1 unit. Does that sound correct?
• Feb 15th 2011, 07:43 PM
pickslides
Quote:

Originally Posted by gbenguse78
I tried that and the graph is the form 1/x. There will be a horizontal translation of 2 units to the left (Vertical Asymptote). It seems the graph will be reflected in the y axis and a vertical translation of 1 unit. Does that sound correct?

Sounds good to me, if you want to see the affect of the dialation, plot some points or even better find some intercepts.
• Feb 15th 2011, 07:47 PM
gbenguse78
Quote:

Originally Posted by pickslides
Sounds good to me, if you want to see the affect of the dialation, plot some points or even better find some intercepts.

Thanks! Really appreciated.