Are my calculations to graph this function [f(x)=(-5x^2+3x)/(2x^2-5)] correct?

[randy17]

Are my calculations to graph this function [f(x)=(-5x^2+3x)/(2x^2-5)] correct?

Can you please check them over and see if I have done this wrong?

 

[srmichael]

Good job! About the only thing that I would have done differently, and this is more to make your eventual sketching of the equation a bit simpler, is to do one number line that includes all the critical points as well as the vertical asymptotes. It helps to see the bigger picture in terms of the max, mins, zeros, etc. Then I would do a separate number line for the concavity part and POI.

 

[DrPhil]

I see the 3rd sheet is page 1, so will start there. intercepts fine, horizontal asymptote fine, positions of VAs fine -
hint on finding signs:
Evaluate the numerator at the pole. That will determine the sign when x approaches the limit from above, and the sign will be opposite when approached from below. The sign of the infinity changes when you cross a simple pole.

I just noticed that srmichael has already responded - makes my response redundant!