Question 1203502
<pre>

{{{graph(400,200,-12,12,-6,6,48/((x-4)(x+4)))}}}

It have vertical asymptotes x=4 and x=-4, so the denominator
must contain (x-4)(x+4).

It has the x-axis as a horizontal asymptote, so the numerator
must be of lower degree than the denominator. so it has the
form: 

{{{f(x)}}}{{{""=""}}}{{{(ax+b)/((x-4)(x+4))}}}

It passes through (0,-3), so f(0) = -3

{{{-3}}}{{{""=""}}}{{{(a(0)+b)/((0-4)(0+4))}}}

{{{-3}}}{{{""=""}}}{{{(b)/(-16))}}}

{{{48=b}}}

It is symmetrical with respect to the y axis, 
therefore f(x) = f(-x)

{{{f(-x)}}}{{{""=""}}}{{{(a(-x)+48)/((-x-4)(-x+48))}}}

So

{{{(ax-48)/((x-4)(x+4))}}}{{{""=""}}}{{{(a(-x)+b)/((-x-4)(-x+4))}}}

{{{ax+48}}}{{{""=""}}}{{{a(-x)+48}}}

{{{ax=-ax}}}

a = -a for all values of x, thus a=0

The equation is

{{{f(x)}}}{{{""=""}}}{{{48/((x-4)(x+4))}}}

The range is (-infinity,-3] U (0,infinity)

Edwin</pre>