Math 141 Exam 3 Preparation Ch3 v01 SPRING 2015 Dressler NO BOOK/ NO NOTES/YES CALCUATOR. Name

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1 Math 141 Eam 3 Preparation Ch3 v01 SPRING 201 Dressler NO BOOK/ NO NOTES/YES CALCUATOR Name Write the quadratic function in the standard form = a( - h)2 + k. 1) = ) 2) = ) 3) = ) 4) = ) Graph the function. ) f() = 2( - 1)( + 2) ) of 22

2 6) f() = ( + 2)( - 3)( + 4) ) ) f() = ) of 22

3 8) f() = ) Find the range of the given function. 9) f() = ) ) f() = ) 11) f() = ) 12) f() = ) 3 of 22

4 Solve the problem. 13) Use the figure to find the width W of the rectangle from its length and area A. Determine W when = 9 ards. 13) W A = Give all possible rational zeros for the polnomial. 14) f() = ) 1) f() = ) 16) f() = ) 17) f() = ) Use Descartesʹs Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 18) f() = ) 19) f() = ) 20) f() = ) 4 of 22

5 21) f() = ) 22) f() = ) 23) f() = ) 24) f() = ) 2) f() = ) Solve the problem. 26) An object is propelled verticall upward from the top of a 224-foot building. The quadratic function s(t) = -16t2 + 80t models the ballʹs height above the ground, s(t), in feet, t seconds after it was thrown. How man seconds does it take until the object finall hits the ground? Round to the nearest tenth of a second if necessar. 26) 27) A bo with an open top is formed b cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides. If represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 13 inches b 11 inches, what size square must be cut if the volume of the bo is to be 126 cubic inches? 27) of 22

6 Simplif. 28) i4 28) 29) i7 29) 30) i 30) 31) i18 31) Find the linear factorization of the polnomial and find all roots of the polnomial. 32) f() = ) 33) f() = ) 34) f() = ) 3) f() = ) 36) f() = ) 6 of 22

7 37) f() = ) Find the product and write the result in standard form. 38) (- - 3i)(3 + i) 38) 39) (4-7i)(- - 2i) 39) 40) (6 + 3i)(6-3i) 40) 41) (-7 + i)(-7 - i) 41) 42) (6 + 9i)2 42) Comple numbers are used in electronics to describe the current in an electric circuit. Ohmʹs law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, b the formula E = IR. Solve the problem using this formula. 43) Find E, the voltage of a circuit, if I = (3 + 9i) amperes and R = (4 + 3i) ohms. 43) 44) Find E, the voltage of a circuit, if I = (18 + i) amperes and R = (3 + 2i) ohms. 44) Write the epression in the standard form a + bi. 4) If z = 9-3i, evaluate z + z. 4) 7 of 22

8 46) If w = 9 + 4i, evaluate w - w. 46) 47) If z = 6 - i, evaluate zz. 47) 48) If z = 3-7i, evaluate 6z. 48) Divide and write the answer in the form a + bi. w 49) Let z = 2 + 2i and w = - 8i. Find z ) 0) Let z = 3 - i and w = -6 - i. Find z + 2i w. 0) 1) Let z = - i and w = i. Find z w. 1) 2) Let z = 7-6i and w = 7 + 4i. Find w z. 2) 3) Let z = 2 + 8i and w = 7-3i. Find w z ) 8 of 22

9 Provide an appropriate response. 4) True or False: The numbers 2 + 3i i and 3-2i are equivalent. 4) ) True or False: The modulus of 7 + 3i is equal to the modulus of 3-7 i. ) Find the indicated intercept(s) of the graph of the function. 6) -intercepts of f() = ) ) -intercepts of f() = ) ( - 2)(2 + 9) 8) -intercepts of f() = ) 9) -intercepts of f() = ) Find the horizontal asmptote, if an, of the graph of the rational function. 8 60) f() = ) 2 61) g() = ) 9 of 22

10 3 62) h() = ) 63) f() = ) 64) h() = ) 6) g() = ) -9 66) f() = ) Find the vertical asmptote(s), if an, of the graph of the rational function. ( + )( - ) 67) h() = ( - 7)( + 6) 67) ) f() = ) 69) f() = 8(2-1)2( + 3) (2-1)( + 3)( - 8) 69) of 22

11 - 4 70) f() = ) Find the values of, if an, where there are holes in the graph of the function. ( + 4)2 71) f() = ) 72) f() = 8(2-1)2 (2-1)( + 6)( - 8) 72) 92(4-3) 73) f() = (4-3)2( + 7)( - 9) 73) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Show all work in the space provided. Match the graph of the rational function with its equation. 74) 74) A) f() = C) f() = B) f() = D) f() = of 22

12 7) 7) A) f() = C) f() = B) f() = D) f() = ) 76) A) f() = C) f() = B) f() = D) f() = of 22

13 77) 77) A) f() = C) f() = B) f() = D) f() = ) 78) A) f() = C) f() = B) f() = D) f() = of 22

14 79) 79) A) f() = C) f() = B) f() = D) f() = ) ) A) f() = C) f() = ( - 2)2 ( + 4)( - 2) B) f() = D) f() = ( + 4)2 ( - 2)( + 4) ( + 2)2 ( - 4)( + 2) 14 of 22

15 81) ) A) f() = C) f() = ( - 2)2 ( + 2)( - 2) ( - 2)2 ( + 2)( - 2) B) f() = D) f() = ( + 2)2 ( - 2)( + 2) Graph the rational function. 2 82) f() = ) of 22

16 4 83) f() = ) ) f() = ) of 22

17 8) f() = ) ) f() = ) of 22

18 4 87) f() = ) ) f() = ) of 22

19 89) f() = ) 4 90) f() = ) of 22

20 - 2 91) f() = ) ) f() = ) 20 of 22

21 93) f() = ) 94) f() = 2-2 ( - )2 94) 21 of 22

22 9) f() = ( - 1)2 9) of 22

23 Answer Ke Testname: EXAM 3PREPARATION CH3 V01 1) = ( - 4) ) = -2( + ) ) = -3( + 2) ) = -3( + 3)2 + 2 ) ) ) of 22

24 Answer Ke Testname: EXAM 3PREPARATION CH3 V01 8) ) (-, -6] ) (-, -6] 11) [8, ) 12) [3, ) 13) 3-4; 23 d 14) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 1) ±1, ± 1, ±3, ±9, ± ) ±1, ± 1 2, ±2, ±3, ± 3 2, ±6, ±9, ± 9 2, ±18 17) ±1, ±11, ± 1 2, ± ) 3 or 1 positive zeros, 2 or 0 negative zeros 19) 2 or 0 positive zeros, 1 negative zero 20) 2 or 0 positive zeros, 1 negative zero 21) 0 positive zeros, 3 or 1 negative zeros 22) 3 or 1 positive zeros, 2 or 0 negative zeros 23) 1 positive zero, 1 negative zero 24) 4, 2 or 0 positive zeros, no negative zeros 2) 1 positive zero, 4, 3 or 1 negative zeros 26) 7.0 seconds 27) 2 in. b 2 in. square 28) 1 29) -i 30) i 31) -1 32) f() = ( + 2i)( - 2i), roots: ± 2i 33) f() = 9( + i)( - i), roots: 0, ± i 34) f() = 2( + 4i)( - 4i), roots: 0, ± 4i 3) f() = ( + 8)( + 3i)( - 3i), roots: -8, ± 3i 36) f() = ( + 2)( + i 3)( - i 3), roots: -2, ± i 3 37) f() = ( - 3)( - 2)( + 4i)( - 4i), roots: 3, 2, ± 4i 38) i 39) i 24 of 22

25 Answer Ke Testname: EXAM 3PREPARATION CH3 V01 40) 4 41) 0 42) i 43) (-1 + 4i) volts 44) (2 + 39i) volts 4) 18 46) 8i 47) 61 48) i 9 49) i 0) i 1) i 2) i 3) i 4) True ) True 6) - 3 2, 0 7) none 8) (2, 0), - 9 2, 0 9) (-1, 0), (2, 0) 60) = 0 61) = 62) no horizontal asmptote 63) = 1 64) = - 1 6) = ) = 0 67) = 7, = -6 68) = 7 69) = 8 70) no vertical asmptote 71) = -4 72) = ) no holes 74) C 7) D 76) D 77) C 78) C 2 of 22

26 Answer Ke Testname: EXAM 3PREPARATION CH3 V01 79) D 80) C 81) B 82) ) ) of 22

27 Answer Ke Testname: EXAM 3PREPARATION CH3 V01 8) ) ) of 22

28 Answer Ke Testname: EXAM 3PREPARATION CH3 V01 88) ) ) of 22

29 Answer Ke Testname: EXAM 3PREPARATION CH3 V01 91) ) ) of 22

30 Answer Ke Testname: EXAM 3PREPARATION CH3 V01 94) ) of 22