# How do you find vertical, horizontal and oblique asymptotes for #y=3/(x-2)+1#?

The vertical asymptote is

The horizontal asymptote is

There is no oblique asymptote.

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To find the vertical asymptote(s), set the denominator of the rational function equal to zero and solve for x.

For the function y = 3/(x - 2) + 1:

x - 2 = 0 x = 2

So, the vertical asymptote is x = 2.

To find the horizontal asymptote, examine the behavior of the function as x approaches positive or negative infinity.

As x approaches positive infinity, y = 3/(x - 2) + 1 approaches 0, because the term with x in the denominator becomes negligible compared to x as x becomes very large. Therefore, the horizontal asymptote is y = 1.

For the oblique asymptote, if the degree of the numerator is one greater than the degree of the denominator, there is an oblique (slant) asymptote. To find it, perform polynomial long division of the numerator by the denominator.

In this case, the degree of the numerator (0) is not greater than the degree of the denominator (1), so there is no oblique asymptote.

In summary:

- Vertical asymptote: x = 2
- Horizontal asymptote: y = 1

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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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