Graphs of Rational Functions (2 of 4)

Learn how to graph rational functions by finding x and y-intercept(s), and vertical and horizontal asymptotes. Domain and range are also discussed.

[davidtutorsmath]

I think I'll reword your question to what I think you mean and then answer it. "Why does the function: (3x^2+10x-8)/(x^2+4) HAVE a horizontal Asymptote?" The most important terms are the 3x^2 on top and x^2 on the bottom (everything else doesn't make as big of a difference). As a result, at the extreme x-values (really big positive x's and really big negative x's) the function values (y-values) approach 3 (Asymptotes: y=3). You can see this happen by actually plugging in the values.