# How do you find the asymptotes for #y= (7x-2) /( x^2-3x-4)#?

The asymptotes of any expression are found by defining what happens to the expression when

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To find the asymptotes of the rational function (y = \frac{{7x - 2}}{{x^2 - 3x - 4}}), follow these steps:

- Determine the degree of the numerator and the denominator.
- If the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at (y = 0).
- If the degree of the numerator equals the degree of the denominator, divide the leading coefficients to find the horizontal asymptote.
- If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. Instead, perform polynomial long division to find any possible slant (oblique) asymptote.
- To find the vertical asymptotes, set the denominator equal to zero and solve for (x). The vertical asymptotes occur where the function is undefined.
- If there are any common factors between the numerator and the denominator, simplify the function before identifying asymptotes.

Follow these steps to find the asymptotes for the given 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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