Simple Graphing rational expressions question

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Homework Help Overview

The discussion revolves around understanding the behavior of rational expressions, specifically focusing on oblique asymptotes and their intersections with the graph of a function.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore how to identify oblique asymptotes and question the conditions under which a graph might intersect these asymptotes.

Discussion Status

Some participants provide insights into determining oblique asymptotes, while others express confusion regarding the nature of intersections between the graph and the asymptote, leading to a debate about the validity of such intersections.

Contextual Notes

There appears to be a misunderstanding regarding the properties of oblique asymptotes, with some participants questioning the assumption that a graph can cross an asymptote.

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

[tex]f(x)=(ax+b) + \frac{g(x)}{h(x)}[/tex]

and then as [tex]x\rightarrow \infty, \frac{g(x)}{h(x)}\rightarrow 0[/tex]
and so [tex]f(x)\rightarrow ax+b[/tex] 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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