p139, #13(a), §2 Graph

Instead of starting to crunch numbers, look at the pieces first:

Factor x²-9=(x-3)(x+3) is a parabola with zeros at :

Squaring gives a quartic with double zeros at :

Dividing by x will produce a simple pole at x=0 and also a sign change at negative x:

Function y(x):

• has an x-extent and a y-extend ;
• is odd (symmetric with respect to the origin);
• has a relative maximum at -3 of finite curvature: ;
• has a relative minimum at 3 of finite curvature: ;
• has a vertical asymptote at x=0 with asymptotic behavior: for ;
• behaves asymptotically as for ;
• is concave up for x>0, down for x<0