1. ## 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.

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

3. 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?

4. 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.

5. 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.