# How do you find the asymptotes for #f(x) = (x+3)/(x^2 + 8x + 15)#?

Only one vertical asymptote is

graph{(x+3)/(x^2+8x+15) [-10, 10, -5, 5]}

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To find the asymptotes for the function (f(x) = \frac{x+3}{x^2 + 8x + 15}), follow these steps:

- Determine if there are any vertical asymptotes by finding the values of (x) for which the denominator is zero. In this case, solve (x^2 + 8x + 15 = 0) to find the roots.
- Factor the denominator, if possible, and then find the roots.
- If there are any horizontal asymptotes, determine them by examining the behavior of the function as (x) approaches positive or negative infinity.
- If there are any slant (oblique) asymptotes, use polynomial division or long division to divide the numerator by the denominator. The quotient obtained will represent the slant asymptote.

After following these steps, you'll have the vertical, horizontal, and slant asymptotes, if they exist, for the function (f(x)).

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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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