SOLUTION: I would really really appreciate any help I could get with the following. R(x)=x^3-1/x^2-x-2 I know how to factor it, but need help with stating the domain and making a graph wit

Algebra ->  Rational-functions -> SOLUTION: I would really really appreciate any help I could get with the following. R(x)=x^3-1/x^2-x-2 I know how to factor it, but need help with stating the domain and making a graph wit      Log On


   

Question 191335: I would really really appreciate any help I could get with the following.
R(x)=x^3-1/x^2-x-2
I know how to factor it, but need help with stating the domain and making a graph with labeled intercepts and asymtotes. Please help. Thanks.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
R(x)=x^3-1/x^2-x-2
I know how to factor it, but need help with stating the domain and making a graph with labeled intercepts and asymtotes
----------------------------------------------------
R(x) = [(x-1)(x^2+x+1)]/[(x-2)(x+1)]
----------------------------------------------
Domain: all Real Numbers except x = 2 and x = -1
-------------------
x-intercept: Let y=0 then x = 1
-----------------------
y-intercept: Let x = 0 then y = -1/-2 = 1/2
------------------------
Vertical asymptotes: x = -1 and at x = 2
------------------
Horizontal asymptote: y = x^3/0x^3 = 1/0; So no horizontal asymptote.
-----------------------------
Graph:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28x%5E3-1%29%2F%28x%5E2-x-2%29%29
==========================================================
Cheers,
Stan H.