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

The most useful thing when trying to draw graphs is to test the zeroes of the function to get some points that can guide your sketch.

graph{1/x -2 [-10, 10, -5, 5]} You should notice that all three of these facts provide enough information to draw the graph above.

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The asymptotes of the function y=1/x-2 are a vertical asymptote at x=2 and a horizontal asymptote at y=0. To graph the function, plot points on the graph by choosing different values for x and calculating the corresponding y-values. Connect the points to form a smooth curve.

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The asymptotes of the function y = 1/(x - 2) are 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 (x = 2) and observe the behavior of the function as x approaches 2. Similarly, plot points for large positive and negative values of x to observe the behavior of the function as x approaches infinity and negative infinity, respectively. Connect these points smoothly, and the resulting graph will show the curve approaching the vertical and horizontal asymptotes.

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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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