let f(x)= (x^2-8x+12)/(x^2+x-2). Consider the end behavior at each asymptote

Question

As x → ∞, y→ _____

As x → −∞, y→ _____

As x → −2^−,y→ _____

As x → −2^+,y→ _____

As x → −2^−,y→ _____

As x → −2^+,y→ _____

Answer 1

You also need to find the horizontal asymptotes. Write the leading term in the numerator over the leading term in the denominator. Simplify and analyze the ratio. If there are no variables left after simplification, you have found your horizontal asymptote(s). If there is still a variable left in either the numerator or the denominator after correct simplification, then look at what happens as x → ∞ . It will either go to zero or go to + or - infinity. If zero, that is your asymptote. If infinity, then the end behavior is not asymptotic.

Answer 2

As I already solved a problem like this, I will let you solve this. All you have to do is factor the numerator and denominator and put the zeroes of the numerator in order in order to determine the intervals and thus whether positive or negative in the intervals, which tells you what happens at the vertical asymptotes. You mean to show -2 and 1, not -2 in both pairs.