When 8-2x=0, that is, when x=4, f(x) is undefined, making x=4 a vertical asymptote. The asymptote divides the curve into two curves on either side of the asymptote, so f(x) is discontinuous. When x<4, f(x)→∞ as x→4; when x>4, f(x)→-∞.
As x gets very large and positive, f(x)→0 but from the negative side (beneath) the x-axis. As x gets large and negative, f(x)→0 but from the positive side (above) the x-axis. Therefore the x-axis is a horizontal asymptote, and the two parts of the curve are divided by the x-axis. So f(x) consists of two parts: to the right of x=4 the whole curve is bounded by and below the x-axis and the line x=4; to the left of x=4 it's bounded by and above the x-axis and the line x=4.