Find the symmetries, horizontal asymptote, max and min and inflection points of
I've already found out the horizontal asymptote and the x and y intercepts.
If we replace with , we get: . . . . the same function
Therefore, the graph is symmetric to the -axis.
Vertical asymptotes occur where the denominator is zero.
. . Hence, and are vertical asymptotes.
For max and min, you need the derivative (quotient rule).
The derivative equals 0 when its numerator is 0: .
To test it, we'll use the Second Derivative Test.
Factor: . 
When . . . positive, concave up:
. . Therefore, a minimum at
Inflection points occur when the second derivative equals zero.
. . But we see from , that cannot equal 0.
Therefore, there are no inflection points.