SOLUTION: y={{{(2-(8/x^2))/(x-(8/x^2))}}}
For this equation I need to give the domain, asymptotes, and removable discontinuities. I get both of the asymptotes but I just have no idea what
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-> SOLUTION: y={{{(2-(8/x^2))/(x-(8/x^2))}}}
For this equation I need to give the domain, asymptotes, and removable discontinuities. I get both of the asymptotes but I just have no idea what
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Question 430397: y=
For this equation I need to give the domain, asymptotes, and removable discontinuities. I get both of the asymptotes but I just have no idea what the domain and removable discontinuities are. :( Please help me! Thank you and have a great day!! Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! One restriction on the value of x is that it should not be equal to 0. Another restriction is that should not be equal to 0. This is the same as saying that should not be equal to 0, is not equal to 0, or x is not equal to 2.
The DOMAIN is then all real numbers not equal to 0 or 2. This said,
.
As x goes to infinity, the expression goes to y = 0, because the degree of the numerator is less than the degree of the denominator. (Because the expression will have no real roots.)
Hence y = 0 is a HORIZONTAL ASYMPTOTE.
Since the denominator is a quadratic irreducible over the real numbers, the expression has NO VERTICAL ASYMPTOTES.
There are REMOVABLE DISCONTINUITIES at x = 0 and x = 2, because they cancel out in the process of simplification. They correspond to "holes" at the graph at the point (0,1) and (2, 2/3).
