3psilon Group Title Help finding ALL asymtotes one year ago one year ago

1. 3psilon Group Title

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

2. josiahh Group Title

$((x-1)(x-2))/((x-1)(x+1))$ $(x-2)/(x+1)$ 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

3. 3psilon Group Title

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

4. josiahh Group Title

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

5. 3psilon Group Title

Do you always do that to find the horizontal asymtote ?

6. josiahh Group Title

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

7. 3psilon Group Title

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

8. josiahh Group Title

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

9. 3psilon Group Title

Ohhhh and if they are equal its Coeffcient over coeffcient?

10. josiahh Group Title

yea that rule...

11. 3psilon Group Title

Thank YOU!

12. josiahh Group Title

welcome