Assignment 3. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Assignment 3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A truck rental company rents a moving truck one day by charging $35 plus $0.09 per mile. Write a 1) linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 200 miles? A) C(x) = 0.09x + 35; $36.80 B) C(x) = 35x ; $ C) C(x) = 0.09x + 35; $53.00 D) C(x) = 0.09x - 35; -$ ) Marty's Tee Shirt & Jacket Company is to produce a new line of jackets with an embroidery of a 2) Great Pyrenees dog on the front. There are fixed costs of $520 to set up for production, and variable costs of $42 per jacket. Write an equation that can be used to determine the total cost, C(x), encountered by Marty's Company in producing x jackets. A) C(x) = ( ) x B) C(x) = 520x + 42 C) C(x) = x D) C(x) = x 3) If an object is dropped from a tower, then the velocity, V (in feet per second), of the object after t 3) seconds can be obtained by multiplying t by 32 and adding 10 to the result. Find V as a linear function of t, and use this function to evaluate V(8.2), the velocity of the object at time t = 8.2 seconds. A) V(8.2) = ft/sec B) V(8.2) = ft/sec C) V(8.2) = ft/sec D) V(8.2) = ft/sec 4) Suppose that a school has just purchased new computer equipment for $18, The school 4) chooses to depreciate the equipment using the straight line method over 5 years. (a) Write a linear function that expresses the book value of the equipment as a function of its age. (b) Graph the linear function. (c) What is the value of the machine after 3 years? 1

2 A) f(x) = -18,000x + 18,000; value after 3 years is -$36, B) f(x) = 18,000x + 5; value after 3 years is $ C) f(x) = 3600x - 18,000; value after 3 years is $ D) f(x) = -3600x + 18,000; value after 3 years is $ ) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.55 as 5) soon as you get in the taxi, to which a charge of $2.20 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride. A) C(x) = x B) C(x) = 3.25x C) C(x) = 4.75x D) C(x) = x Determine the slope and y-intercept of the function. 6) F(x) = x 6) A) m = 0; b = B) m = 1 4 ; b = 0 C) m = -4; b = 0 D) m = ; b = 0 2

3 7) Linda needs to have her car towed. Little Town Auto charges a flat fee of $60 plus $3 per mile 7) towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 9 miles. A) c(x) = 3x; $63 B) c(x) = 3x + 60; $87 C) c(x) = 3x + 60; $77 D) c(x) = 3x; $27 8) A lumber yard has fixed costs of $ per day and variable costs of $0.06 per board-foot 8) produced. Lumber sells for $1.56 per board-foot. How many board-feet must be produced and sold daily to break even? A) 86,175 board-feet B) 3447 board-feet C) 2298 board-feet D) 3191 board-feet 9) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.60 as 9) soon as you get in the taxi, to which a charge of $2.45 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride, and use this equation to find the cost of a 7-mile taxi ride. A) $19.63 B) $20.65 C) $19.75 D) $19.93 Graph the function. State whether it is increasing, decreasing, or constant.. 10) h(x) = -4x ) A) decreasing B) increasing 3

4 C) increasing D) decreasing Find the vertex and axis of symmetry of the graph of the function. 11) f(x) = -8x2-2x ) A) -8, ; x = -8 B) 1 8, 39 8 ; x = 1 8 C) (8, -5); x = 8 D) - 1 8, ; x = Graph the function using its vertex, axis of symmetry, and intercepts. 12) f(x) = x2-6x ) A) vertex (-3, -4) intercepts (-5, 0), (- 1, 0), (0, 5) B) vertex (-3, 4) intercepts (-5, 0), (- 1, 0), (0, -5) 4

5 C) vertex (3, -4) intercepts (5, 0), (1, 0), (0, 5) D) vertex (3, 4) intercepts (5, 0), (1, 0), (0, -5) Find the vertex and axis of symmetry of the graph of the function. 13) f(x) = -3x2 + 24x 13) A) (-4, 48); x = -4 B) (-4, 0); x = -4 C) (4, 0); x = 4 D) (4, 48); x = 4 14) The owner of a video store has determined that the profits P of the store are approximately given 14) by P(x) = -x2 + 30x + 76, where x is the number of videos rented daily. Find the maximum profit to the nearest dollar. A) $526 B) $301 C) $450 D) $225 15) A projectile is fired from a cliff 600 feet above the water at an inclination of 45 to the horizontal, 15) with a muzzle velocity of 200 feet per second. The height h of the projectile above the water is given by h(x) = -32x 2 + x + 600, where x is the horizontal distance of the projectile from the base of (200)2 the cliff. Find the maximum height of the projectile. A) ft B) ft C) ft D) 625 ft Graph the function using its vertex, axis of symmetry, and intercepts. 16) f(x) = 2x2 + 8x ) 5

6 A) vertex (-2, 5) intercept 0, 7 B) vertex (2, 5) intercept (0, 13) C) vertex (2, 5) intercept 0, 7 D) vertex (-2, 5) intercept (0, 13) Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 17) f(x) = x2-6 17) A) maximum; 0 B) minimum; 0 C) minimum; -6 D) maximum; -6 18) f(x) = 4x2-12x 18) 3 3 A) minimum; B) maximum; - 9 C) minimum; - 9 D) maximum; 2 2 Find the vertex and axis of symmetry of the graph of the function. 19) f(x) = x2-6x 19) A) (3, -9); x = 3 B) (-9, 3); x = -9 C) (9, -3); x = 9 D) (-3, 9); x = -3 6

7 Determine the domain and the range of the function. 20) f(x) = -x2 + 2x ) A) domain: all real numbers range: {y y -4} C) domain: all real numbers range: {y y 4} B) domain: {x x -1} range: {y y 4} D) domain: all real numbers range: all real numbers 21) The owner of a video store has determined that the cost C, in dollars, of operating the store is 21) approximately given by C(x) = 2x2-26x + 780, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar. A) $696 B) $611 C) $442 D) $865 22) The cost in millions of dollars for a company to manufacture x thousand automobiles is given by 22) the function C(x) = 4x2-40x Find the number of automobiles that must be produced to minimize the cost. A) 100 thousand automobiles B) 5 thousand automobiles C) 10 thousand automobiles D) 20 thousand automobiles Use a graphing calculator to plot the data and find the quadratic function of best fit. 23) A small manufacturing firm collected the following data on advertising expenditures (in 23) thousands of dollars) and total revenue (in thousands of dollars). Advertising, x Total Revenue, R Find the quadratic function of best fit. A) R(x) = x x B) R(x) = x x C) R(x) = x x D) R(x) = -0.31x x ) A projectile is thrown upward so that its distance above the ground after t seconds is 24) h = -11t t. After how many seconds does it reach its maximum height? A) 40 sec B) 10 sec C) 30 sec D) 20 sec 7

8 25) A projectile is fired from a cliff 500 feet above the water at an inclination of 45 to the horizontal, 25) with a muzzle velocity of 210 feet per second. The height h of the projectile above the water is given by h(x) = -32x 2 + x + 500, where x is the horizontal distance of the projectile from the base of (210)2 the cliff. Find the maximum height of the projectile. A) ft B) ft C) ft D) ft Use a graphing calculator to plot the data and find the quadratic function of best fit. 26) The following table shows the median number of hours of leisure time that Americans had each 26) week in various years. Year Median # of Leisure hrs per Week Use x = 0 to represent the year Using a graphing utility, determine the quadratic regression equation for the data given. What year corresponds to the time when Americans had the least time to spend on leisure? A) M(x) = 0.021x2-1.44x ; 1989 B) M(x) = x x ; 1989 C) M(x) = 0.04x2-1.21x ; 1988 D) M(x) = -0.04x x ; ) You have 112 feet of fencing to enclose a rectangular plot that borders on a river. If you do not 27) fence the side along the river, find the length and width of the plot that will maximize the area. A) length: 28 ft, width: 28 ft B) length: 56 ft, width: 28 ft C) length: 84 ft, width: 28 ft D) length: 56 ft, width: 56 ft 28) If g(x) = x2-2x - 3, solve g(x) 0. 28) A) {x x 3}; [3, ) B) {x -1 x 3}; [-1, 3] C) {x x -1 or x 3}; (-, -1] or [3, ) D) {x x -1}; (-, -1] Solve the inequality. 29) x2-11x + 30 > 0 29) A) {x x > 6}; (6, ) B) {x x < 5}; (-, 5) C) {x x < 5 or x > 6}; (-, 5) or (6, ) D) {x 5 < x < 6}; (5, 6) 30) 2x2-9 < -3x 30) A) x 3 2 < x < 3 ; 3 2, 3 B) x < x < 3 ; - 3 2, 3 C) x -3 < x < ; -3, D) x -3 < x < 3 2 ; -3, 3 2 8

9 31) x ) A) [-16, 16] B) {x x -4 or x 4}; (-, -4] or [4, ) C) (-, -16] or [16, ) D) {x -4 x 4}; [-4, 4] 32) x2-6x 0 32) A) {x x 0 or x 6}; (-, 0] or [6, ) B) {x 0 x 6}; [0, 6] C) {x x -6 or x 0}; (-, -6] or [0, ) D) {x -6 x 0}; [-6, 0] 33) If f(x) = 6x2-5x and g(x) = 2x + 3, solve f(x) g(x). 33) A) x x 3 2 ; - 1 3, 3 B) x x 1 3 ; - 3 2, 1 3 C) x < x < 3 2 ; - 1 3, 3 2 D) x < x 3 2 ; - 1 3, 3 2 Solve the inequality. 34) x2 + 2x 0 34) A) {x x -2 or x 0}; (-, -2] or [0, ) B) {x -2 x 0}; [-2, 0] C) {x 0 x 2}; [0, 2] D) {x x 0 or x 2}; (-, 0] or [2, ) 35) A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired 35) with an initial velocity of 128 feet per second, and the gorge is 240 feet deep, during what interval can the flare be seen? (h = -16t2 + v0t + h0.) A) {t 9 < t < 11}; (9, 11) B) {t 6 < t < 8}; (6, 8) C) {t 0 < t < 3}; (0, 3) D) {t 3 < t < 5}; (3, 5) 9