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

Vertical asymptote:

Graph - Rectangular hyperbola as below.

graph{1/(x-2) [-10, 10, -5, 5]}

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The function y=1/(x-2) has two asymptotes: a vertical asymptote at x=2 and a horizontal asymptote at y=0. To graph the function, plot points on either side of the vertical asymptote and observe the behavior of the function as x approaches positive and negative infinity. Additionally, plot the point (2,0) on the graph.

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The asymptotes of ( y = \frac{1}{x-2} ) are the vertical and horizontal asymptotes.

Vertical asymptote: ( x = 2 ) Horizontal asymptote: ( y = 0 )

To graph the function:

- Plot the vertical asymptote at ( x = 2 ).
- Determine the behavior of the function as ( x ) approaches positive and negative infinity to sketch the horizontal asymptote at ( y = 0 ).
- Choose several points on either side of the vertical asymptote and calculate their corresponding ( y ) values to plot points.
- Sketch the curve passing through the plotted points, making sure it approaches the asymptotes as ( x ) approaches positive and negative infinity.

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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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- How do you simplify the rational expression #(x^3+x^2)/(x+1)#?

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