# What are the asymptotes for #y=3/(x-1)+2# and how do you graph the function?

Vertical Asymptote is at

Horizontal Asymptote is at

Graph of the rational function is available with this solution.

We are given the rational function

We will simplify and rewrite

Hence,

Vertical Asymptote

Set the denominator to Zero.

So, we get

Hence,

Vertical Asymptote is at

Horizontal Asymptote

We must compare the degrees of the numerator and denominator and verify whether they are equal.

To compare, we need to deal with lead coefficients.

The lead coefficient of a function is the number in front of the term with the highest exponent.

If our function has a horizontal asymptote at

where

Hence,

Horizontal Asymptote is at

Graph of the rational function with the horizontal asymptote and the vertical asymptote can be found below:

I hope you find this solution with the graph useful.

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The asymptotes for the function y=3/(x-1)+2 are a vertical asymptote at x=1 and a horizontal asymptote at y=2. To graph the function, plot the vertical asymptote at x=1 and draw a dashed line. Then, plot a few points on either side of the vertical asymptote and connect them with a smooth curve. Finally, draw the horizontal asymptote at y=2 as a dashed line.

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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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