Find Horizontal Asymptote of Rational Function F(x)

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Discussion Overview

The discussion centers around finding the horizontal asymptote of the rational function F(x) = (6x^2 - 17x - 3) / (3x + 2). Participants explore the concept of horizontal asymptotes in relation to this specific function, including potential misunderstandings about the function's notation.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant clarifies the function notation, suggesting it should be written as f(x) = (6x^2 - 17x - 3) / (3x + 2).
  • Another participant explains that a horizontal asymptote is a line that a function approaches but does not reach, providing an example of y=0 for f(x) = e^x.
  • There is a claim that there are no horizontal asymptotes for the given function, but a vertical asymptote exists where 3x + 2 = 0.
  • One participant notes the potential for a diagonal asymptote, contingent on whether such concepts have been covered in the OP's studies.

Areas of Agreement / Disagreement

Participants express differing views on the existence of horizontal asymptotes for the function, with some asserting there are none while others suggest further clarification is needed regarding the function's notation and possible asymptotic behavior.

Contextual Notes

There is ambiguity in the function's notation, which may affect the interpretation of its asymptotic properties. Additionally, the discussion does not resolve the question of whether diagonal asymptotes have been taught to the OP.

shorty888
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F(x)= 6x^2-17x-3/3x+2, find horizontal asymptote
 
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shorty888 said:
F(x)= 6x^2-17x-3/3x+2, find horizontal asymptote

Do you mean $f(x) = \frac{6x^2-17x-3}{3x+2}$

A horizontal asymptote is a line where a function approaches but doesn't quite reach there. An example is y=0 for f(x) = e^x

There are no horizontal asymptotes in your case, there is a vertical one where 3x+2 = 0 but no horizontal ones.

nb: Please take care with brackets, I've guessed at what you meant but that isn't the literal meaning of what you wrote which would be $F(x) = 6x^2-17x-x+2$
 
Yes I mean fraction

shorty888 said:
F(x)= 6x^2-17x-3/3x+2, find horizontal asymptote
 
SuperSonic4 said:
Do you mean $f(x) = \frac{6x^2-17x-3}{3x+2}$

A horizontal asymptote is a line where a function approaches but doesn't quite reach there. An example is y=0 for f(x) = e^x

There are no horizontal asymptotes in your case, there is a vertical one where 3x+2 = 0 but no horizontal ones.

nb: Please take care with brackets, I've guessed at what you meant but that isn't the literal meaning of what you wrote which would be $F(x) = 6x^2-17x-x+2$
There is also a diagonal asymptote but a word from the OP will be required to find out if such asymptotes have been taught.
 

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