An oblique asymptote is a line that a curve approaches but never touches as it extends to infinity. It is not a part of the graph itself, but rather describes its behavior at the extreme ends.
If the equation of a curve contains a term with y², the oblique asymptote will be a diagonal line with a slope equal to the coefficient of the y² term. This is because as y approaches infinity, the y² term becomes dominant and the curve behaves more like a straight line with a slope of y².
In this case, the oblique asymptote will still be a diagonal line, but the slope will be the ratio of the coefficient of y² and the coefficient of 1/y. This is because as y approaches infinity, the y² term will dominate and the 1/y term will become negligible.
Yes, it is possible for a curve to have more than one oblique asymptote. This can occur when the equation of the curve contains multiple terms with y² and/or 1/y. Each term will contribute to the overall slope of the asymptote.
To graph a curve with an oblique asymptote, we first plot the points of the curve and then sketch the asymptote. The curve should approach the asymptote as it extends to infinity, but never touch or cross it. It is also helpful to plot a few additional points to better visualize the behavior of the curve near the asymptote.