Behavior of Polynomial Functions for Large Values of x: Figure 15-3g shows f(x) = x3 7x2

Chapter 15, Problem 11

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Behavior of Polynomial Functions for Large Values of x: Figure 15-3g shows f(x) = x3 7x2 + 10x + 2 (solid) and g(x) = x3 (dashed) The graph on the right is zoomed out by a factor of 4 in the x-direction and by a factor of 64 (equal to 43) in the y-direction. Figure 15-3g a. Plot the two graphs on your grapher with a window as shown in the graph on the left. Set the zoom factors on your grapher to 4 in the x-direction and 64 in the y-direction. Then zoom out by these factors. Does the result resemble the graph on the right in Figure 15-3g? b. Zoom out again by the same factors. Sketch the resulting graphs. c. What do you notice about the shapes of the two graphs as you zoom out farther and farther? Can you still see the intercepts and vertices of the f graph? What do you think is the reason for saying that the highestdegree term dominates the function for large values of x?