# How do you find the asymptotes for #f(x) = 5/(x - 7) + 6#?

The asymptotes correspond to the excluded values:

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To find the asymptotes for the function f(x) = 5/(x - 7) + 6, we need to consider two types of asymptotes: vertical asymptotes and horizontal asymptotes.

Vertical asymptotes occur when the denominator of the function becomes zero. In this case, the denominator is (x - 7). Setting it equal to zero, we find x - 7 = 0, which gives us x = 7. Therefore, the vertical asymptote is x = 7.

Horizontal asymptotes can be determined by analyzing the behavior of the function as x approaches positive or negative infinity. In this case, as x approaches positive or negative infinity, the function approaches the value of 6. Hence, the horizontal asymptote is y = 6.

To summarize, the asymptotes for the function f(x) = 5/(x - 7) + 6 are a vertical asymptote at x = 7 and a horizontal asymptote at y = 6.

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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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