Math 3

math 3.rtfd/TXT.rtf

 Question 1

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Find the indicated intercept(s) of the graph of the function. x-intercepts of f(x) = f1q42g1.jpg ¬

spacer.gif ¬ (9, 0)(-9, 0)(0, 0) and (-9, 0)(0, 0) and (9, 0)

1__#$!@%!#__spacer.gif ¬   Question 2

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Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = x4 + 6x3 + 17x2 + 54x + 72

2__#$!@%!#__spacer.gif ¬ f(x) = (x - 4)(x + 2)(x - 3)(x + 3)f(x) = (x + 4)(x + 2)(x - 3i)(x + 3i)f(x) = (x - 1)(x - 8)(x - 3i)(x + 3i)f(x) = (x - if1q77g1.jpg ¬)(x + if1q77g2.jpg ¬)(x - 3)(x +3)

3__#$!@%!#__spacer.gif ¬   Question 3

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State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 4(x - 1)12(x + 1)9

4__#$!@%!#__spacer.gif ¬ Yes; degree 48Yes; degree 21Yes; degree 4Yes; degree 12

5__#$!@%!#__spacer.gif ¬   Question 4

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Find the x- and y-intercepts of f. f(x) = (x + 2)(x - 3)(x + 3)

6__#$!@%!#__spacer.gif ¬ x-intercepts: -3, 3, 2; y-intercept: 18x-intercepts: -2, -3, 3; y-intercept: 18x-intercepts: -3, 3, 2; y-intercept: -18x-intercepts: -2, -3, 3; y-intercept: -18

7__#$!@%!#__spacer.gif ¬   Question 5

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Give the equation of the oblique asymptote, if any, of the function. f(x) = f1q49g1.jpg ¬

8__#$!@%!#__spacer.gif ¬ y = x - 3x = y - 3y = x - 9no oblique asymptotes

9__#$!@%!#__spacer.gif ¬   Question 6

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Find the indicated intercept(s) of the graph of the function. y-intercept of f(x) = f1q1g1.jpg ¬

10__#$!@%!#__spacer.gif ¬ (0, 3)(0, 4)f1q1g2.jpg ¬f1q1g3.jpg ¬

11__#$!@%!#__spacer.gif ¬   Question 7

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Determine where the function is increasing and where it is decreasing. f(x) = -x2 - 4x + 5

12__#$!@%!#__spacer.gif ¬ increasing on (-∞, 9) decreasing on (9, ∞)increasing on (-2, ∞) decreasing on (-∞, -2)increasing on (-∞, -2) decreasing on (-2, ∞)increasing on (9, ∞) decreasing on (-∞, 9)

13__#$!@%!#__spacer.gif ¬   Question 8

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Use the graph to find the horizontal asymptote, if any, of the function. f1q108g1.jpg ¬

14__#$!@%!#__spacer.gif ¬ y = 0x = 2y = 3y = 0, y = 3

15__#$!@%!#__spacer.gif ¬   Question 9

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For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x) = f1q53g1.jpg ¬4(x - 1)3

16__#$!@%!#__spacer.gif ¬ - f1q53g2.jpg ¬, multiplicity 4, touches x-axis; 1, multiplicity 3, crosses x-axisf1q53g3.jpg ¬, multiplicity 4, touches x-axis; -1, multiplicity 3, crosses x-axisf1q53g4.jpg ¬, multiplicity 4, crosses x-axis; -1, multiplicity 3, touches x-axis- f1q53g5.jpg ¬, multiplicity 4, crosses x-axis; 1, multiplicity 3, touches x-axis

17__#$!@%!#__spacer.gif ¬   Question 10

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Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. f(x) = (x - 2)2(x + 4)2

18__#$!@%!#__spacer.gif ¬ above the x-axis: (-4, 2) below the x-axis: (-∞, -4), (2, ∞)above the x-axis: no intervals below the x-axis: (-∞, -4), (-4, 2), (2, ∞)above the x-axis: (-∞, -4), (2, ∞) below the x-axis: (-4, 2)above the x-axis: (-∞, -4), (-4, 2), (2, ∞) below the x-axis: no intervals

19__#$!@%!#__spacer.gif ¬   Question 11

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Solve. While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger experiences a force of 162 newtons when the car is moving at a speed of 60 kilometers per hour and the passenger has a mass of 50 kilograms, find the force a passenger experiences when the car is moving at 40 kilometers per hour and the passenger has a mass of 100 kilograms.

20__#$!@%!#__spacer.gif ¬ 128 newtons144 newtons160 newtons176 newtons

21__#$!@%!#__spacer.gif ¬   Question 12

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Use the graph to find the vertical asymptotes, if any, of the function. f1q5g1.jpg ¬

22__#$!@%!#__spacer.gif ¬ x = -3, x = 3, x = 0x = -3, x = 3, y = 0nonex = -3, x = 3

23__#$!@%!#__spacer.gif ¬   Question 13

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Solve the equation in the real number system. 2x4 - 2x3 + x2 - 5x - 10 = 0

24__#$!@%!#__spacer.gif ¬ {-1, 2}f1q54g1.jpg ¬{1, -2}f1q54g2.jpg ¬

25__#$!@%!#__spacer.gif ¬   Question 14

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Give the equation of the horizontal asymptote, if any, of the function. f(x) = f1q116g1.jpg ¬

26__#$!@%!#__spacer.gif ¬ y = 2y = 6y = 1no horizontal asymptotes

27__#$!@%!#__spacer.gif ¬   Question 15

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Find the vertex and axis of symmetry of the graph of the function. f(x) = -5x2 - 2x - 2

28__#$!@%!#__spacer.gif ¬ f1q22g1.jpg ¬; x = -5f1q22g2.jpg ¬; x = f1q22g3.jpg ¬(5, -2); x = 5f1q22g4.jpg ¬; x = - f1q22g5.jpg ¬

29__#$!@%!#__spacer.gif ¬   Question 16

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Solve. The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate f1q26g1.jpg ¬ of power when f1q26g2.jpg ¬ of current is flowing through the resistor whose resistance is f1q26g3.jpg ¬ find the power that a resistor needs to dissipate when f1q26g4.jpg ¬ of current are flowing through a resistor whose resistance is f1q26g5.jpg ¬

30__#$!@%!#__spacer.gif ¬ 63 watts147 watts84 watts21 watts

31__#$!@%!#__spacer.gif ¬   Question 17

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Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = x3 + 8x2 + 22x + 20

32__#$!@%!#__spacer.gif ¬ f(x) = (x + 2)(x + 3 + i)(x + 3 - i)f(x) = (x + 2)(x + 3 + i)(x - 3 - i)f(x) = (x - 1)(x + 3 + if1q10g1.jpg ¬)(x + 3 - if1q10g2.jpg ¬)f(x) = (x + 1)(x + 3 + if1q10g3.jpg ¬)(x - 2 - if1q10g4.jpg ¬)

33__#$!@%!#__spacer.gif ¬   Question 18

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Solve the inequality. (x + 1)(x - 3) ≤ 0

34__#$!@%!#__spacer.gif ¬ (-∞, -1][-1, 3][3, ∞)(-∞, -1] or [3, ∞)

35__#$!@%!#__spacer.gif ¬   Question 19

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Solve the inequality. f1q32g1.jpg ³ 0

36__#$!@%!#__spacer.gif ¬ (-∞, -7) or [-2, 6) or [12, ∞)(-∞, -7) or [12, ∞)(-7, -2] or (6, 12](-∞, -7) or [-2, 0) or (0, 6) or [12, ∞)

37__#$!@%!#__spacer.gif ¬   Question 20

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Form a polynomial whose zeros and degree are given. Zeros: -1, 1, - 2; degree 3

38__#$!@%!#__spacer.gif ¬ f(x) = x3 - 2x2 + x - 2 for a = 1f(x) = x3 - 2x2 - x + 2 for a = 1f(x) = x3 + 2x2 + x + 2 for a = 1f(x) = x3 + 2x2 - x - 2 for a = 1

39__#$!@%!#__spacer.gif ¬ 40__#$!@%!#__spacer.gif ¬ 41__#$!@%!#__spacer.gif ¬ 42__#$!@%!#__spacer.gif ¬ 43__#$!@%!#__spacer.gif ¬ 44__#$!@%!#__spacer.gif ¬ 45__#$!@%!#__spacer.gif ¬ 46__#$!@%!#__spacer.gif ¬ 47__#$!@%!#__spacer.gif ¬ 48__#$!@%!#__spacer.gif ¬ 49__#$!@%!#__spacer.gif ¬ 50__#$!@%!#__spacer.gif ¬ 51__#$!@%!#__spacer.gif ¬ 52__#$!@%!#__spacer.gif ¬ 53__#$!@%!#__spacer.gif ¬ 54__#$!@%!#__spacer.gif ¬ 55__#$!@%!#__spacer.gif ¬ 56__#$!@%!#__spacer.gif ¬ 57__#$!@%!#__spacer.gif ¬ 58__#$!@%!#__spacer.gif ¬ 59__#$!@%!#__spacer.gif ¬ 60__#$!@%!#__spacer.gif ¬ 61__#$!@%!#__spacer.gif ¬ 62__#$!@%!#__spacer.gif ¬ 63__#$!@%!#__spacer.gif ¬ 64__#$!@%!#__spacer.gif ¬ 65__#$!@%!#__spacer.gif ¬ 66__#$!@%!#__spacer.gif ¬ 67__#$!@%!#__spacer.gif ¬ 68__#$!@%!#__spacer.gif ¬ 69__#$!@%!#__spacer.gif ¬ 70__#$!@%!#__spacer.gif ¬ 71__#$!@%!#__spacer.gif ¬ 72__#$!@%!#__spacer.gif ¬ 73__#$!@%!#__spacer.gif ¬ 74__#$!@%!#__spacer.gif ¬ 75__#$!@%!#__spacer.gif ¬ 76__#$!@%!#__spacer.gif ¬ 77__#$!@%!#__spacer.gif ¬ 78__#$!@%!#__spacer.gif ¬ 79__#$!@%!#__spacer.gif ¬