# How do you find the asymptotes for #Q(x) = (2x^2)/ (x^2 - 5x - 6)#?

vertical asymptotes x = -1 , x = 6

horizontal asymptote y = 2

Vertical asymptotes occur when the denominator of a rational function tends to zero. To find the equation/s let the denominator equal zero.

Here is the graph of the function. graph{(2x^2)/(x^2-5x-6) [-20, 20, -10, 10]}

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To find the asymptotes of the function ( Q(x) = \frac{2x^2}{x^2 - 5x - 6} ):

- Identify the vertical asymptotes by finding the values of ( x ) for which the denominator becomes zero. These are the values that make the function undefined.
- Identify the horizontal asymptotes by examining the behavior of the function as ( x ) approaches positive or negative infinity. If the degrees of the numerator and the denominator are equal, the horizontal asymptote is the ratio of the leading coefficients.
- If there are any slant (oblique) asymptotes, determine them by performing polynomial long division if the degree of the numerator is one greater than the degree of the denominator.

Once you have found the vertical, horizontal, and slant asymptotes, you have identified all the asymptotes of the function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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