In the text we said that a line is an asymptote for a

Chapter 1, Problem 51

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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, well 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, youll see that the curve is virtually indistinguishable from an asymptote when either x 8 or y 8. 52.