Alg_Complete

X 2 multiplicity 1 x0 x2 multiplicity 3 multiplicity

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Unformatted text preview: ints that we pick aren’t really all that important. We just want to pick points according to the guidelines in the process outlined above and points that will be fairly easy to evaluate. Here are some points. We will leave it to you to verify the evaluations. P ( -2 ) = -320 P (1) = -20 P ( 3) = 80 Now, to actually sketch the graph we’ll start on the left end and work our way across to the right end. First, we know that on the left end the graph decreases without bound as we make x more and more negative and this agrees with the point that we evaluated at x = -2 . So, as we move to the right the function will actually be increasing at x = -2 and we will continue to increase until we hit the first x-intercept at x = 0 . At this point we know that the graph just touches the x-axis without actually crossing it. This means that at x = 0 the graph must be a turning point. The graph is now decreasing as we move to the right. Again, this agrees with the next point that we’ll run across, the y-intercept. Now, according...
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