Asymptotes and graphs

This will have vertical asymptotes as well as a "slant" asymptote....

The  y  ...and x....   intercept is at x  = 0

It will be defined everywhere except at the x values that make the denominator  = 0

We can find these values as follows :

x^2 -  3  = 0

x^2  = 3    take both roots

x  = ± √3     the graph will have vertical asymptotes at these values

To find the asymptote ......    divide x^3  b x^2 - 3 and disregard any remainder

                      x

x^2 - 3     [    x^3           ]

                     x^3 - 3x

                             3x 

So.....the asymptote is  y  = x

There are other Calculus techniques involved in graphing this...but, let's cut to the chase.....you can see it here :    https://www.desmos.com/calculator/gedjottav7

Thank you!!