MHB Find Horizontal Asymptote of Rational Function F(x)

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The function F(x) = (6x^2 - 17x - 3) / (3x + 2) does not have a horizontal asymptote. Instead, it has a vertical asymptote where 3x + 2 = 0. The discussion highlights the importance of proper notation, as misinterpretation can lead to confusion about the function's form. Additionally, there may be a diagonal asymptote, but clarification from the original poster is needed to determine if this concept has been covered in their studies. Understanding these asymptotic behaviors is crucial for analyzing rational functions.
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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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