Question

Help finding ALL asymtotes

Answer 1

of \[y = \frac{ x^2 - 3x + 2 }{ x^{2}-1 }\]

Answer 2

\[((x-1)(x-2))/((x-1)(x+1))\]
\[(x-2)/(x+1)\]
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

Answer 3

I'm not really understanding the horizontal asymtote part :(

Answer 4

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

Answer 5

Do you always do that to find the horizontal asymtote ?

Answer 6

yea. horizontal retricemptotes describe the behavior of the graph as x increases

Answer 7

@josiahh Doing it algebraically I'm not so good with limits So can you show me algebraically how the limit = 1 please?

Answer 8

when you are taking limits at infinity, you look at the degree of the polynomials in the denominator and the numerator

Answer 9

Ohhhh and if they are equal its Coeffcient over coeffcient?

Answer 10

yea that rule...

Answer 11

Thank YOU!

Answer 12

welcome