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3psilon
Help finding ALL asymtotes
of \[y = \frac{ x^2 - 3x + 2 }{ x^{2}-1 }\]
\[((x-1)(x-2))/((x-1)(x+1))\] \[(x-2)/(x+1)\] you have vertical asymptote at x=-1 horizontal asymptotes at negative infinity and positive infinity y=1 is your horizontal asymptote for both infinities x=-1 is your only vertical one because you canceled out the (x-1) factor
I'm not really understanding the horizontal asymtote part :(
you take limit as x approaches infinity and negative infinity. when you do that, you get 1. limit x approaches negative infinity = limit x approaches infinity =1
Do you always do that to find the horizontal asymtote ?
yea. horizontal retricemptotes describe the behavior of the graph as x increases
@josiahh Doing it algebraically I'm not so good with limits So can you show me algebraically how the limit = 1 please?
when you are taking limits at infinity, you look at the degree of the polynomials in the denominator and the numerator
Ohhhh and if they are equal its Coeffcient over coeffcient?