determine the horizontal and vertical asymptotes of the function f(x) = 1/(4-x^2) and sketch the graph of f(x)...

my attempts to the question :

i rearrange the graph f(x) = 1/-(x^2-4) ==> 1/-((x-2)(x+2))

so it has two vertical assymptotes which are x = -2 and 2. is there any horizontal assymptote??? huhuhu

by using the conventional method to sketch the graph the graph of f(x) can be obtained by :

1. reflecting graph 1/x^2 by y-axis and shift the graph 4 unit to the right...

but when i sketch the graph of f(x) by using gc it looks like in the figure...

since in the exam we are not allow to bring gc, is there any other ways to sketch the graph??? or my way to treat this question is wrong??? PLZ HELP ME...