SOLUTION: what is the horizantal aymptotes of y=4/x-2+3

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Question 404617: what is the horizantal aymptotes of y=4/x-2+3
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The horizontal asymptotes of y+=+4%2F%28x-2%29+%2B+3 occur when lim%28x-%3Einfinity%2C+4%2F%28x-2%29+%2B+3%29 or lim%28x-%3E-infinity%2C+4%2F%28x-2%29+%2B+4%29 are defined (this is just the formal way of saying that when x gets really large, the value of y is a finite number).

In this case, since the degree in the denominator is larger, lim%28x-%3Einfinity%2C+4%2F%28x-2%29%29+=+0 and lim%28x-%3E-infinity%2C+4%2F%28x-2%29%29+=+0. Since the expression converges, we can add three to each limit and obtain 3 as our horizontal asymptotes. We can check by graphing the function, if we wish:

graph%28300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C+4%2F%28x-2%29+%2B+3%2C+3%29