In the text we said that a line is an asymptote for a curve if the distance between the li...

In the text we said that a line is an asymptote for a curve if the distance between the line and the curve approaches zero as we move farther and farther out along the line. In terms of graphing, this means that as we zoom out, the curve and the line eventually appear indistinguishable. In this exercise, we’ll demonstrate this using the curve y = −4/x (which we graphed in Figure 9). As indicated in the text, both the x- and y-axes are asymptotes for this curve. First, graph y = −4/x using a viewing rectangle that extends from −5 to 5 in both the x- and the y-directions. Then take a second look using a viewing rectangle that extends from −30 to 30 in both the x- and y-directions. At this scale, you’ll see that the curve is virtually indistinguishable from an asymptote when either |x| > 8 or |y| > 8.

Figure 9

The graph of y = −4/x is symmetric about the origin.