David W. answered • 06/16/15
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The line defined by x=2 is vertical because y=any rational value. Thus this y is not a function.
The function y=r(x) in the problem doesn’t have a value for x=2, but rather has a “vertical asymptote” at x=2. This means that the value of y = r(x) as x approaches 2 is either y approaches +∞ or y approaches –∞.
The function y=r(x) in the problem doesn’t have a value for x=2, but rather has a “vertical asymptote” at x=2. This means that the value of y = r(x) as x approaches 2 is either y approaches +∞ or y approaches –∞.
Billy J.
Thank you.
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06/16/15
Andrew M.
Note that for there to be a vertical asymptote at x=2 then the original equation has (x-2) in the denominator. The asymptote exists because we cannot divide by zero. That means the function can approach the point x=2 but never actually touch it... So the y value at x=2 either rises towards infinity or falls towards negative infinity.
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06/16/15
David W.
Dear Mark M. and Andrew W.
I think that I wrote that "the line defined by x=2 is vertical" ... and ... "thus is not a function." Of course, the y=r(x) of the problem is a function and asymptotically approaches that line.
p.s., Being unambiguous and being misunderstood and posting errors and posting corrections is lots more fun than answering student's questions.
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06/17/15
Mark M.
06/16/15