Find all of the asymptotes of f(x) = 3x2 − 1x2 + x − 6. Note that there may be more than one correct answer. (Select all that apply.)
Question
Find all of the asymptotes of
f(x) = \frac{3x^2 - 1}{x^2 + x - 6}.
Note that there may be more than one correct answer. (Select all that apply.)
Solution
The function you've given is f(x) = 3x^2 - 1x^2 + x - 6. However, it seems like there might be a mistake in the function. If we simplify it, we get f(x) = 2x^2 + x - 6.
To find the asymptotes of a function, we first need to determine the type of function. In this case, it's a polynomial function. Polynomial functions do not have vertical or horizontal asymptotes. They may have oblique (slant) asymptotes if the degree of the numerator is exactly one more than the degree of the denominator. However, in this case, there is no denominator, so there are no asymptotes.
So, the correct answer is that there are no asymptotes for the given function.
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