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

Answer 1

Hazel Anglin

Below

#y=3/(x-1)-2# can be rewritten as:

#y=-2+3/(x-1)#

Domain: all real x except #x=1# Range: all real y except #y=-2#

The domain and range are both found by letting y approach 0 and x approach 0 respectively.

First, you would draw in your dotted lines with the equation #x=1# and #y=-2#. Then you would find whether or not the ends of your graph approaches the top or bottom of the asmpytotes.

graph{3/(x-1)-2 [-10, 10, -5, 5]}

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Answer 2

Julia Adams

The asymptotes of 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 as a dashed line. Then, plot 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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Answer from HIX Tutor

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.