Let f(x) (x3 2x2 1)/(x2 2x). (a) Graph the function f

Chapter 4, Problem 52

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Let f(x) (x3 2x2 1)/(x2 2x). (a) Graph the function f using a viewing rectangle extending from 5 to 5 in both the x- and y-directions. (b) Add the graph of the line y x to your picture in part (a). Note that to the right of the origin, as x increases, the graph of f begins to look more and more like the line y x. This also occurs to the left of the origin as x decreases. (c) The results in part (b) suggest that the line y x may be an asymptote for the graph of f. Verify this visually by changing the viewing rectangle so that it extends from 20 to 20 in both the x- and the y-directions. What do you observe? (d) Using algebra, verify the identity Then explain why, for large values of x , the graph of f looks more and more like the line y x. Hint: Substitute some large numbers (such as 100 or 1000) into the expression 1/(x2 2x). What happens? 53. L