Posted by Mae on Sunday, October 5, 2008 at 8:31pm.
the culprit for asymptotes and holes is the denominator.
If for some value of the variable, then denominator is zero, but the numerator is NOT zero, you will have an asymptote.
If for some value of the variable, then denominator is zero, but the numerator is ALSO zero, you will have a hole
e.g. y = (x-2)/(x^2 - 4)
notice this reduces to y = 1/(x+2)
so if x = 2 in the original we get 0/0, so there is a hole at (2,1/4)
if x = -2 we get -4/0 in the original, so x = -2 is an asymptote
how would we know if it has both holes and asymptotes?
What is the domain and range of 2x^2-18/x^2+3x-10
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