Assignment 3.3, 3.4, 3.5. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Assignment 3.3, 3.4, 3.5 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. 1) 3x8 + 6x6 + 6x4 + 5x2 + 9 = 0 1) A) Positive (4), negative (0) B) Positive (4), negative (4) C) Positive (0), negative (0) D) Positive (0), negative (4) TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Determine whether the statement is true or false. 2) If f(x) is a polynomial having only real coefficients and 3-5i is a zero of f(x), then x - 3-5i is a 2) factor of f(x). MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a polynomial of lowest degree with only real coefficients and having the given zeros. 3) 3 + 3, 3-3, and 3 3) A) f(x) = x3-11x2 + 24x + 18 B) f(x) = x3 + 9x2 + 24x - 18 C) f(x) = x3-9x2 + 24x - 18 D) f(x) = x3-11x2 + 24x + 20 Use the factor theorem to decide whether or not the second polynomial is a factor of the first. 4) 3x2-3x + 18; x - 2 4) A) No B) Yes For the polynomial, one zero is given. Find all others. 5) P(x) = x3-3x2 + 7x - 5; 1 5) A) 1 + 5, 1-5 B) i, -1-2i C) 1 + 2i, 1-2i D) 1 + 5i, 1-5i Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. 6) Zeros of -2, 1, 0 and P(2) = 32 6) A) P(x) = 4x2 + 4x - 8 B) P(x) = 4x3-4x2-8x C) P(x) = 4x3 + 4x2-8x D) P(x) = 4x3 + 12x2-8x For the polynomial, one zero is given. Find all others. 7) P(x) = x4-32x2-144; -2i 7) A) 2i, 12i, -12i B) 2i, 12, -12 C) 2i, 6, -6 D) 2i, 6i, -6i 1

2 Solve the problem. 8) The following polynomial approximates the shark population in a particular area. 8) R(x) = x x , where x is the number of years from Use a graphing calculator to describe the rabbit population from the years 1940 to A) The population decreases. B) The population remains stable. C) The population increases. Solve. 9) The concentration of a certain gas molecule in the atmosphere serves as an indicator of industrial 9) air pollution. The data in the following table show the relationship of the estimated concentration of the molecule in the atmosphere, in parts per billion (ppb), to the year. Year Concentration (ppb) Take 1985 as year zero, and determine the linear, quadratic, or cubic function that best fits the data. A) f(x) = x x x B) f(x) = 0.002x C) f(x) = x x D) f(x) = x x ) The price of electric guitars has varied considerably in recent years. The data in the table relates the 10) price P, in dollars, to time t, in years, where t = 1 corresponds to Use a cubic function fitted to the data to predict the price of an electric guitar in Average price, p, Year, t of an electric guitar 1988 (t = 1) $ (t = 2) (t = 3) (t = 4) (t = 5) (t = 6) (t = 7) (t = 8) (t = 9) A) $ B) $ C) $ D) $ Find the correct end behavior diagram for the given polynomial function. 11) P(x) = 1.38x4 + 3x2 + x ) A) B) C) D) 2

3 Solve. 12) A biking club has increased its membership each year since its founding in The table 12) provides membership data for several years. Year # of Members Take 1985 as year zero, and determine the linear, quadratic, cubic, or quartic function that best fits the data. A) f(x) = x x x B) f(x) = 0.94x C) f(x) = 0.003x4-0.98x x D) f(x) = x x Find the equation that the given graph represents. 13) 13) A) P(x) = -x3 + 15x2 + x - 10 B) P(x) = -x5-5x3-6x2 + 10x C) P(x) = x5 + 3x4-5x3-15x2 + x + 10 D) P(x) = x4-5x3 + 6x2 + x + 10 Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. 14) f(x) = x4-9x ) A) -1, 2.7, 2.7, -2.7 B) 5, -5, 4, -4 C) 2.2, 2 D) 2.2, -2.2, 2, -2 Answer the question 15) How can the graph of f(x) = 1 x - 5 be obtained from the graph of y = 1 x? 15) A) By making a horizontal shift of 5 units to the right B) By making a vertical shift of 5 units down C) By making a horizontal shift of 5 units to the left D) By making a vertical shift of 5 units up 3

4 1 16) How can the graph of f(x) = (x - 3)2 + 2 be obtained from the graph of y = 1 x2? 16) A) By making a horizontal shift of 3 units to the right and a vertical shift of 2 units up B) By making a horizontal shift of 2 units to the left and a vertical shift of 3 units up C) By making a horizontal shift of 2 units to the right and a vertical shift of 3 units down D) By making a horizontal shift of 3 units to the left and a vertical shift of 2 units down Determine which of the rational functions given below has the following feature(s). 5 17) x-intercepts: -5 and -1, y-intercepts:, vertical asymptote: x = 4, horizontal asymptote: y = 1 17) 16 A) f(x) = C) f(x) = (x - 5)(x - 1) (x + 4) (x - 5)(x - 1) (x + 4)2 B) f(x) = D) f(x) = (x + 5)(x + 1) (x - 4)2 (x + 5)(x + 1) (x - 4) Find any vertical asymptotes. 3x ) h(x) = x2 + 3x ) A) x = 1, x = -4 B) x = -1, x = 4 C) y = 1, y = -4 D) y = 3 4

5 Graph the function. 2x 19) f(x) = x2 + 4x ) A) B) C) D) Solve the problem. 20) In the following formula, f(x) is the minimum number of hours of studying required to attain a test 20) score of x: f(x) = 0.38x. How many hours of study are needed to score 85? x A) 2.08 hr B) 5.17 hr C) hr D) hr 5