The vertical asymptotes are found by looking at the denominator and finding out what value(s) of x make it zero. x^2=0 has two solutions: x=-2 and 2. These are vertical lines. The horizontal asymptote applies when x gets very large and approaches plus or minus infinity. At these values the function approximates to 1/x, because the other numbers are small by comparison. 1/x gets smaller and smaller approaching zero, which is the horizontal x axis asymptote. You don't really need to draw the graph. It has two parts: the left side sits under the x axis and starts at the extreme left nearly touching the axis then it curves around to point downwards to almost touch the line x=-2. The other half is in the positive region above the x axis, nearly touching it on the extreme right and bending up to head towards the line x=2.