Name. 3) f(x) = -x2-2. Sketch the graph of the function and find the domain and range. 1) f(x) = x2-4. 4) f(x) = x ) f(x) = -3(x + 3)2-2

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1 Exam 3 Final Preparation Ch 7, 9, etal v0 There will be 5 questions on Exam 3 (Final). Twenty questions from chapters 7 & 9. Five questions from chapter 5. No Book/No Notes/No Ipod/ No Phone/Yes Calculator/55 minutes Name 3) f(x) = -x - Sketch the graph of the function and find the domain and range. 10 y 1) f(x) = x y x x -10 4) f(x) = x y ) f(x) = -3(x + 3) - y x x of 15

2 Solve the problem. 5) A parabola has a y-intercept of (0, 5). The x-coordinate of its vertex is 11. Use symmetric points to find another point on the parabola. 10) (x + 3) = 5 11) x + 5 = ) Find the x-coordinate of the vertex of a parabola passing through the points (-8, -3) and (18, -3). 1) (m + 3) - 11 = 38 7) Find the x-coordinate of the vertex of a parabola passing through the points (0, -8) and (-18.8, -8). 13) 5(y - 1) + 11 = 75 8) Find the x-coordinate of the vertex of a parabola having x-intercepts (-9, 0) and (15, 0). 14) (6x - ) - 3 = - Solve. 9) (x + 11) = 15) 5(y - 1) + 15 = 96 of 15

3 Simplify. 16) -5 Find all complex number solutions. ) x = -9 17) ) x = -4 18) -80 4) x + 6 = 0 19) ) (x - 4) = -11 0) ) x = ) ) -(y - 1) + 17 = 66 3 of 15

4 Find all complex-number solutions by completing the square. 8) x - 4x + 13 = 0 Find the x-intercepts of the function. 34) f(x) = x - 6x - 7 9) y - 8y = -4 35) g(x) = x + 18x ) x + x + 1 = 0 36) h(x) = x + 1x ) 5x - 5x + 3 = 0 37) f(x) = x + 7x + 3 3) 6x + 5x + 8 = 0 38) f(x) = x + 7x ) 3 p p = 0 39) f(x) = x + 7x of 15

5 Use the quadratic formula to solve the given equation. 40) x = 8x + 3 Find all complex-number solutions by using the quadratic formula. 46) y - 1y = ) 15x = -10x 47) x + x + 5 = 0 4) 7x - 13 = 0 48) -16x = -7x ) x + 1x = ) 6x - 9x + 8 = 0 44) -3x + x = -3 50) x - 5 x = ) 1 x x = 0 51) -16x = -5x of 15

6 Solve by the method of your choice. 5) 9x = 4 58) m = 16m ) 4x - 8 = 0 59) 5x - 9x - = 0 54) x - 11x - 6 = 0 60) (x - 4)(x + 3) = 4(x - 1) ) (x + 5)(x - 1) = 8 61) (x - ) = ) 5x = -8x - 1 6) -7(y - 1) + 18 = 54 57) (x + 14)(x - 15) = 4(x - 1) ) 4x - 3x = -7 6 of 15

7 64) (x - 3) = -175 Determine the number and type of solutions. 70) x + 5x + 6 = 0 65) (x - ) = ) x + 6x + 9 = 0 66) -(y - 1) + 16 = 65 7) 8x = -5x ) y + 16y = -7 73) + 6x = 3x 68) -5(y - 1) + 16 = 5 74) 6-4x = x ) -5(y - 1) + 15 = 79 75) 3x + 9x = of 15

8 76) x - 14x + 58 = 0 77) x + 1x + 36 = 0 78) 9x - 71x - 8 = 0 Solve the problem. 8) The following table shows the median number of hours of leisure time per week for Americans in various years. Year Median Number of Leisure Hours per W Let f(t) be the median number of hours of leisure time at t years since The data can be modeled by the quadratic model f(t) = 0.04t - 1.1t Use the model to estimate the year when the median number of hours of leisure time was the smallest. 79) 7x - 55x - 8 = 0 80) 5x + 9x + 5 = 0 83) An object is propelled vertically upward from the top of a 80-foot building. The quadratic function s(t) = -16t + 11t + 80 models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. After how many seconds does the object reach its maximum height? Round to the nearest tenth of a second if necessary. 81) 6x + 5x + 6 = 0 84) You have 104 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. 8 of 15

9 85) The owner of a video store has determined that the profits P of the store are approximately given by P(x) = -x + 150x + 56, where x is the number of videos rented daily. Find the maximum profit to the nearest dollar. 86) The daily profit in dollars of a specialty cake shop is described by the function P(x) = -5x + 0x - 190, where x is the number of cakes prepared in one day. The maximum profit for the company occurs at the vertex of the parabola. How many cakes should be prepared per day in order to maximize profit? 88) Not all murder cases are solved. The percentages of murder cases solved in various years are listed in the table below. Year Percent of Cases Solved (Source: Bureau of Justice Statistics) Let f(t) represent the percent of murder cases solved at t years since A reasonable model is f(t) = 0.0t t Find the approximate vertex of f. What does it mean in terms of the situation?. 87) The sales for a gaming console for various years are listed in the table below. Sales Year (in billions of dollars) Let f(t) represent the sales (in billions of dollars) at t years since A reasonable model is f(t) = 0.065t t According to the model, when were sales at a minimum? What were the sales in that year? Find the inverse of the given function. 89) 5 x 90) log 5 (x) 91) 3 x 9 of 15

10 Solve the problem. 9) An object is propelled vertically upward from the top of a 16-foot building. The quadratic function s(t) = -16t + 144t + 16 models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. After how many seconds does the object reach its maximum height? Round to the nearest tenth of a second if necessary. 96) x7/3 97) 3x4y8 5/4 93) You have 64 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. 98) 5 x8y13 94) The owner of a video store has determined that the profits P of the store are approximately given by P(x) = -x + 90x + 58, where x is the number of videos rented daily. Find the maximum profit to the nearest dollar. Simplify the expression. Assume that all variables are non-negative. 99) 8x7y8 100) 15 (x4yz3) 5 If the expression is in exponential form, write it in radical form. If it is in radical form, write it in exponential form. 95) x1/ 101) (x + )8 10 of 15

11 Simplify. Assume that each variable is nonnegative. 10) 4x 8x 108) (9 x + 8 )( x - 6) 103) 3 x ( 3 4x x5 ) Simplify the expression. Assume that all variables are non-negative. 109) ) ( 3 + z)( 3 - z) 110) 4 65x8y16 105) ( 3 - x )( 4 - x ) 111) 5 xy 106) ( x - 5 y4 )( 8x + 5 y4) Solve. 11) x = 4 107) (5 x + )( 5x - ) 11 of 15

12 113) 3 3x = ) x - 3 = x ) x + = - 10) 4 x + 8 = 4 3x 115) - 4x + 5 = -5 11) x + 9 = 5x ) 3 4x = 0 Find all x-intercepts. 1) h(x) = 8x ) 7x - 5 = 6x ) g(x) = 7x - 5-6x ) x x = 0 14) k(x) = x x of 15

13 Solve for the specified variable. Assume that the constants have values for which the equation has exactly one real-number solution. 15) r = 3V πh, for V Evaluate. 130) Let g(x) = 3x. Find g() 131) Let g(x) = 5x. Find g-1(15) 16) r = A, for θ. θ 13) Let f(x) = log 4 (x). Find f(16) 17) x = r - y, for r. 133) Let f(x) = log 3 (x). Find f-1(3) 18) q = p p + 1, for p. 134) Let f(x) = log 5 (x). Find f-1() 19) H = F F + G, for F. Solve. If necessary, round the answer to two decimal places. 135) log 8 (5) + log 8 (x) = 1 13 of 15

14 136) log (3) + log (x) = 0 14) e(x + 8) = 6 137) log 3 (x - 4) + log 3 (x - 10) = 3 143) ln (6x) + ln (3x) = 5 138) log 1 (x + 84) + log 1 (x) = 3 144) ln (x) + 3 ln (7x3) = 5 139) log (3x - ) - log (x - 5) = 4 145) ex - 5 e4x = ) log 6 (x + 6) + log 6 (x) = 3 146) e(x + 5) = 7 Solve the equation. Round the solution to four decimal places, if necessary. 141) e5x = 3 Simplify. Write the expression as a single logarithm with a coefficient of ) ln (x) + ln (5x) 14 of 15

15 148) ln (x) + 4 ln (5x) 154) 3 ln (w) - ln (8w8) 149) 6 ln(a) - 8 ln(b) 155) 3 ln(x - 11) - 7 ln(x) 150) 9 ln(a) - 7 ln(b) 156) 3 ln (x) + ln (6x) 151) 11 ln(x - 6) - 7 ln(x) 157) 3 ln (w) - ln (8w9) 15) 3 ln(x - 8) - 11 ln(x) 158) 3 ln (x) + 4 ln (3x) 153) 3 ln (x) + 4 ln (6x) 159) ln (w) - ln (6w8) 15 of 15

16 Answer Key Testname: EXAM 3 FINAL PREPARATION CH 7, 9, ETALV0 1) domain: all real numbers range: y y x ) domain: all real numbers range: y - 10 y x ) domain: all real numbers range: y - 10 y x of 15

17 Answer Key Testname: EXAM 3 FINAL PREPARATION CH 7, 9, ETALV0 4) domain: all real numbers range: y y x ) (, 5) 6) 5 7) ) 3 9) -11 ± 10) -3 ± 5 11) - ± ) 4, ) 5 ± ) 1, ) 5 ± ) 15i 17) -5i 18) i 70 19) i 13 0) i ) -10i ) ±3i 3) ± i 6 4) ± i 13 5) 4-11i, i 6) -4 ± i of 15

18 Answer Key Testname: EXAM 3 FINAL PREPARATION CH 7, 9, ETALV0 7) ± 7i 8) x = ± 3i 9) 4 ± i 30) -1 ± i 3 31) 5 ± i ) -5 ± i ) 5 ± i ) (7, 0), (-1, 0) 35) (-9-11, 0), ( , 0) 36) (-6-6, 0), (-6 + 6, 0) 37) -7-37, 0, , 0 38) 39) -7-1, 0, -7-9, 0, , , 0 40) 4 ± 19 41) - 3, 0 4) ± ) -6 ± 6 44) 1 ± ) -1 ± ) 6 ± 8i 5 47) -1 ± i 19 48) 7 ± i ) 9 ± i ) ± i ) 5 ± i of 15

19 Answer Key Testname: EXAM 3 FINAL PREPARATION CH 7, 9, ETALV0 5) ± 3 53) ± 7 54) - 1, 6 55) - ± 56) -4 ± ) - 4, ) 8 59) - 1 5, 60) 1, 4 61) ± 7i 6) 7 ± 6i ) 3 ± i ) 3 ± 5i 7 65) ± 7i 5 66) ± 7i 67) -8 ± i 68) 5 ± 6i ) 5 ± 8i ) real solutions 71) 1 real solution 7) imaginary solutions 73) imaginary solutions 74) real solutions 75) real solutions 76) imaginary solutions 77) 1 real solution 78) real solutions 79) real solutions 80) imaginary solutions 81) imaginary solutions 8) ) 3.5 sec 84) length: 5 ft, width: 6 ft 85) $ ) cakes 19 of 15

20 Answer Key Testname: EXAM 3 FINAL PREPARATION CH 7, 9, ETALV0 87) 1995; $17 million 88) (13.8, 64.47); 64.47% of cases were solved in 1993, which is the lowest percent for any year. 89) log 5 (x) 90) 5 x 91) log 3 (x) 9) 4.5 sec 93) length: 3 ft, width: 16 ft 94) $083 95) x 96) 3 x ) 3x 4y8 98) (x8y13) 1/5 99) x3y4 x 100) 3 x4yz3 101) (x + )4 10) 4x 7x 103) x x 3 14x 104) 3 - z 105) 1-7 x + x 106) 8x - 7x 5 y4 - y 5 y3 107) 5x 5-10 x + 5x ) 9x - 46 x ) ) 5xy4 111) 10 xy 11) ) ) empty set 115) 5 116) ) ) ) -, 3 10) 4 11) 1, 8 1) (7, 0) 13) (10, 0) 14) no x-intercepts 0 of 15

21 Answer Key Testname: EXAM 3 FINAL PREPARATION CH 7, 9, ETALV0 15) V = πr h 3 16) θ = A r 17) r = x + y 18) p = 19) F = 130) 9 131) 3 13) 133) 7 134) 5 135) 8 5 q 1 - q GH 1 - H 136) ) ) ) 6 140) 1 141) ) ) ) ) ) ) ln (5x6) 148) ln (65x8) 149) ln a 6 b8 150) ln a 9 b7 151) ln (x - 6) 11 x7 15) ln (x - 8) 3 x11 153) ln (196x10) 1 154) ln 8w 155) ln (x - 11) 3 x7 1 of 15

22 Answer Key Testname: EXAM 3 FINAL PREPARATION CH 7, 9, ETALV0 156) ln (36x8) 1 157) ln 8w3 158) ln (81x10) 1 159) ln 6w4 of 15