SOLUTION: First, Graph: f(x) =x^2+2/x^2+x-2 Then: Identify Vertical Asymptotes: Algebraic Verification: Identify Horizontal Asymptotes: Algebraic Verification: Identify Obl

Algebra ->  Graphs -> SOLUTION: First, Graph: f(x) =x^2+2/x^2+x-2 Then: Identify Vertical Asymptotes: Algebraic Verification: Identify Horizontal Asymptotes: Algebraic Verification: Identify Obl      Log On


   

Question 1028105: First, Graph: f(x) =x^2+2/x^2+x-2
Then:
Identify Vertical Asymptotes:
Algebraic Verification:
Identify Horizontal Asymptotes:
Algebraic Verification:
Identify Oblique Asymptote:
Algebraic verification:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) =x^2+2/x^2+x-2

f%28x%29+=x%5E2%2B2%2Fx%5E2%2Bx-2 OR f%28x%29+=%28x%5E2%2B2%29%2F%28x%5E2%2Bx-2%29 ?

The second definition is assumed in this work.

First, here is the graph, simply applying the graphing code for the site:
graph%28400%2C400%2C-6%2C6%2C-6%2C6%2C%28x%5E2%2B2%29%2F%28x%5E2%2Bx-2%29%29

Factorize numerator and denominator completely, at least for Real number purposes.

f%28x%29=%28x%5E2%2B2%29%2F%28%28x-1%29%28x%2B2%29%29

No hole since no factor is common between numerator and denominator.

Undefined for x=1 and x=-2, so this causes vertical asymptotes.

Degree of numerator and denominator both EVEN and EQUAL, so as x tends unbounded in either direction, f approaches 1. Horizontal asymptote y=1.

Try polynomial long division. You will find 1 plus some rational expression, consistant with what is found as the horizontal asymptote. NO oblique asymptote!