Simple Graphing rational expressions question

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To find the point where a graph crosses an oblique asymptote, one must first understand that the oblique asymptote represents the behavior of the function as x approaches infinity. The function can be expressed in the form f(x)=(ax+b) + g(x)/h(x), where g(x)/h(x) approaches zero as x increases. However, the discussion clarifies that the oblique asymptote itself does not contain any points of the graph; it does not intersect with the graph. Therefore, the graph does not cross the oblique asymptote at any point. Understanding this distinction is crucial for analyzing rational functions.
xCanx
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How do you find the point where the graph crosses the oblique asymptote?
 
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If you mean how to find an oblique asymptote of a function. you basically get it into the form

f(x)=(ax+b) + \frac{g(x)}{h(x)}

and then as x\rightarrow \infty, \frac{g(x)}{h(x)}\rightarrow 0
and so f(x)\rightarrow ax+b and that it is the oblique asymptote
 
I know how to find the oblique asymptote, but my question was how to find the point on the oblique asymptote where the graph crosses.

When it switches sides.
 
xCanx said:
I know how to find the oblique asymptote, but my question was how to find the point on the oblique asymptote where the graph crosses.

When it switches sides.
Unreasonable. The asymptote contains no point of the graph; the asymptote does not intercept the graph.
 
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