Lesson 17-Quiz 4 (25 points) I

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Lesson 17-Quiz 4 (25 points) I. For each of the following, sketch a graph of the function by transforming the graph of a function of the form J ( x) = x n • In each case, explain why you drew the graph that you did. (2 points each) a). g(x) = 2x 3 -3 b). g(x)=(x+I)4-2 2. For each of the following, sketch a graph of the polynomial function. In each case, by discussing things such as end behavior and multiplicity of roots, explain why you drew the graph that you did. (2 points each) a) h(x) = x 3 -x 2 -6x b) h(x)=x3(x-2)(x+I) c) h(x)=(x+l) 2 (x-7) 2 3. Determine a polynomial of degree four whose graph resembles that shown below. (2 points) y X 4. For each of the following, find the quotient and remainder when P ( x) is divided by D ( x) . (2 points each) a) P(x) b) P(x) =x2 =x4 5. Factor P(x) + 2x + 7; D(x) + x =x6 6. Factor P ( x) = x P(x). (4 points) 4 3 =x -1 + 2x 2 + x +I; D(x) - 8x 4 + 6x 3 + 7 x - x 3 - 2 - =x2 - 2x + I 6x completely. (3 points) 6 x 2 completely, and sketch the graph of 7. Find a fourth-degree polynomial with zeros at x = 0, I, - 2 , where the zero of I has multiplicity 2, and such that the leading coefficient is 7. (2 points)