SOLUTION: Analyze and graph the function {{{(x^2+x-12)/(x+2)}}}. Please provide the steps I must take in order to solve this.

Algebra ->  Rational-functions -> SOLUTION: Analyze and graph the function {{{(x^2+x-12)/(x+2)}}}. Please provide the steps I must take in order to solve this.       Log On


   

Question 771271: Analyze and graph the function %28x%5E2%2Bx-12%29%2F%28x%2B2%29. Please provide the steps I must take in order to solve this.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2%2Bx-12%29%2F%28x%2B2%29 fully factorable to
%28x-3%29%28x%2B4%29%2F%28x%2B2%29

Performing polynomial division of the expression in the originally given form, the quotient will be x-1-10%2F%28x%2B2%29, giving a slant asymptote of y=x-1. Vertical asymtpote is at x=-2 becasue the denominator must not be zero (the denominator of the given expression).

Two zeros occur: x=-4, and x=3 are the zeros of the function.

Critical points are x at -4, -2, and 3. These are the intervals along the horizontal axis. ...
x%3C-4
-4%3Cx-2
-2%3Cx%3C3
3%3Cx
What you want to do is test any x value in each interval and find if the function is positive or negative. I omit that part of the analysis, but this is the graph:

graph%28400%2C400%2C-8%2C8%2C-8%2C8%2C%28x%5E2%2Bx-12%29%2F%28x%2B2%29%29

OR THIS

graph%28500%2C500%2C-15%2C15%2C-15%2C15%2C%28x%5E2%2Bx-12%29%2F%28x%2B2%29%29