# How do you find the slant asymptotes for #(x^2-6x+7)/(x+5)#?

Your function has a first asymptote (vertical) at

The other asymptote can be found as follows:

And graphically:

hope it helps

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To find the slant asymptotes for the function ( \frac{x^2 - 6x + 7}{x + 5} ):

- Perform polynomial long division to divide (x^2 - 6x + 7) by (x + 5).
- The quotient obtained will represent the linear portion of the function.
- If the quotient is of the form (ax + b), where (a) and (b) are constants, then the equation of the slant asymptote is (y = ax + b).

Performing the polynomial long division:

(x^2 - 6x + 7) divided by (x + 5) yields (x - 11) with a remainder of 62.

Therefore, the slant asymptote is (y = x - 11).

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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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