1. Oct 16, 2007

### ming2008

I do not know how to use horizontal , vertical , oblique asymptotes to graph a rathional functions.

like y=2x+3+3/x+1;
y=x^2-4/x-4

thank you very much

2. Oct 17, 2007

### HallsofIvy

Well, this was posted yesterday so I imagine it is too late. (Please do not expect people to be sitting around waiting for you to post something. We do have lives.)

The first thing you need to do is write the equations properly. Surely you do not actually mean "y= 2x+ 3+ (3/x)+ 1" or "y= x^2- (4/x)-4" which is what you wrote! Use parentheses: y= 2x+ 3+ 3/(x+1)? or y= (x^2-4)/(x-4) ?

You need to look at places where the denominator of any fraction is 0. Those will be, in general, vertical asymptotes. You should also look for places where the entire function is equal to 0. Those will be places where the graph crosses the x-axis. Finally, by checking the sign of f(x) for a single x-value in each interval between such points, you can get a rough idea of what the graph looks like between.