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- Thread starter BananaJoe
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In summary, the conversation discusses the concept of oblique asymptotes for a function and whether a function without any remainder after polynomial division is considered to have an oblique asymptote. The definition of an asymptote is also questioned, using the example of g(x)=x+1 being an asymptote to f(x)=x+1. The conversation also clarifies the notation used and asks for further explanation on certain terms.

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As in, is g(x)=x+1 an asymptote to f(x)=x+1?

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I'm having a hard time understanding what you're asking.BananaJoe said:

"where the x^n+1/x^n or any" - what does this mean?

Also, the expression you wrote probably isn't what you meant. What you wrote is this:

x

I can't tell if you meant ##\frac{x^{n + 1}}{x^n}## or ##\frac{x^n + 1}{x^n}##. Suitably placed parentheses would be a great help.

"perfect match wihout any Rests" - ??

An oblique asymptote is a type of asymptote that is not horizontal or vertical, but instead takes on a slanted or diagonal form on a graph.

Polidiv, or polynomial long division, is a method used to divide polynomials. When dividing a polynomial function by a linear function, the resulting quotient will be the equation of the oblique asymptote.

The oblique asymptote can help determine the end behavior of a function and provide useful information for graphing the function.

Yes, an oblique asymptote can intersect the graph of a function at most once. This intersection point is known as a removable discontinuity.

Yes, there are other methods such as synthetic division and the use of limits. However, polidiv is typically the most commonly used method in finding oblique asymptotes.

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