MHB Find Horizontal Asymptote of Rational Function F(x)

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SUMMARY

The function F(x) = (6x^2 - 17x - 3) / (3x + 2) does not have a horizontal asymptote. Instead, it has a vertical asymptote at x = -2/3, where the denominator equals zero. The discussion also mentions the possibility of a diagonal asymptote, contingent on the original poster's familiarity with such concepts. Proper notation is crucial for clarity in mathematical expressions.

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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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