Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 4.1 Polynomial Functions and Models
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Summary of the Properties of the Graphs of Polynomial Functions
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Figure 3
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Figure 6
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Find a polynomial of degree 3 whose zeros are -4, -2, and 3. Use a graphing utility to verify your result.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. For the polynomial, list all zeros and their multiplicities. 2 is a zero of multiplicity 1 because the exponent on the factor x – 2 is 1. –1 is a zero of multiplicity 3 because the exponent on the factor x + 1 is 3. 3 is a zero of multiplicity 4 because the exponent on the factor x – 3 is 4.
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y = 4(x - 2)
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. y = 4(x - 2)
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Figure 16 (a)
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Figure 16 (b)
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Figure 16 (c)
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Figure 16 (d)
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The polynomial is degree 3 so the graph can turn at most 2 times.
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Figure 22
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. The domain and the range of f are the set of all real numbers.
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A cubic relation may exist between the two variables. Table 8
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Cubic function of best fit: Table 8
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Cubic function of best fit: