As x goes to -inf, the numerator goes to 0, and the denominator goes to -infinity. Both make f(x) go to 0. Since f is negative, this happens in the 3rd quadrant. So the x-axis is an asymptote.
As x goes to 0, the numerator goes to 1, but f goes to -infinitity for negative x, and +infinity for positive x, so the y-axis is an asymptote.
As x goes to +infinity, the f(x) gets arbitrarily large, but there is no asymptote.
I don't understand your second part. What is y doing in there? If it's a constant, you just have a parabola, which has no asymptotes. If f is a function of two variables, I don't know what "asymptotes" means in that context. If it was supposed to be an x, then f(x) = 3/4 = a constant, but isn't defined at x=0. I think you must have mistyped something.
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As x goes to -inf, the numerator goes to 0, and the denominator goes to -infinity. Both make f(x) go to 0. Since f is negative, this happens in the 3rd quadrant. So the x-axis is an asymptote.
As x goes to 0, the numerator goes to 1, but f goes to -infinitity for negative x, and +infinity for positive x, so the y-axis is an asymptote.
As x goes to +infinity, the f(x) gets arbitrarily large, but there is no asymptote.
Here's a graph. I've limited the absolute value of f to 20 so that the scale won't go off the charts as x gets close to 0. http://i276.photobucket.com/albums/kk2/freond1/exo...
I don't understand your second part. What is y doing in there? If it's a constant, you just have a parabola, which has no asymptotes. If f is a function of two variables, I don't know what "asymptotes" means in that context. If it was supposed to be an x, then f(x) = 3/4 = a constant, but isn't defined at x=0. I think you must have mistyped something.