SOLUTION: I'm trying to graph f(x)=x/x^2+1 I need to include all the intercepts and asymptotes. I worked out that the horizontal asymptote is y=0 and that the y-intercept is (0,0). I'm ha

Algebra ->  Rational-functions -> SOLUTION: I'm trying to graph f(x)=x/x^2+1 I need to include all the intercepts and asymptotes. I worked out that the horizontal asymptote is y=0 and that the y-intercept is (0,0). I'm ha      Log On


   

Question 241541: I'm trying to graph f(x)=x/x^2+1
I need to include all the intercepts and asymptotes. I worked out that the horizontal asymptote is y=0 and that the y-intercept is (0,0). I'm having problems with the rest, though.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
You've done very well so far. You've found all there is to find except
  • since f(-x) = -f(x), the graph will be symmetric about the origin.
  • if you know Calculus, you can find
    • local maximum and minimum points, if any
    • where the graph is increasing and where it is decreasing
    by finding and using the first and second derivatives.
  • you can build a table of values and plot the points.

Here's a graph:
graph%28400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+x%2F%28x%5E2%2B1%29%29