Test Bank for Calculus for Business, Economics, Life Sciences, and Social Sciences, 14th Edition

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ExamName___________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use point-by-point plotting to sketch the graph of the equation.1)y=x+51)A)B)C)D)1

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2)y=x2+12)A)B)C)D)2

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Determine whether the graph is the graph of a function.3)3)A)functionB)not a functionDetermine whether the function is linear, constant, or neither4)y=x+374)A)LinearB)ConstantC)NeitherUse point-by-point plotting to sketch the graph of the equation.5)f(x)=2xx+25)A)B)3

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C)D)The graph of a function f is given. Use the graph to answer the question.6)Use the graph of f given below to find f(-50).50-5050-506)A)80B)0C)-50D)30Find the function value.7)Find f(-6) when f(x)=9-3x2.7)A)117B)-99C)27D)45Determine the domain of the function.8)f(x)=-7x+98)A)No solutionB)All real numbersC)xK97D)All real numbers except97Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of xto which there corresponds more than one value of y.9)x-y2=99)A)A function with domain[B)Not a function; for example, when x=10, y=±14

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Solve the problem.10)The function F described by F(x)=2.75x+71.48 can be used to estimate the height, in centimeters,of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate theheight of a woman whose humerus is30.93 cmlong. Round your answer to the nearest fourdecimal places.10)A)43.3000 cmB)156.5375 cmC)105.1600 cmD)13.5775 cmGive the domain and range of the function.11)f(x)=x2+211)A)Domain: all real numbers; Range:[2,Q)B)Domain: [2,Q); Range: all real numbersC)Domain: [0,Q); Range: [0,Q)D)Domain: all real numbers; Range:[3,Q)Provide an appropriate response.12)How can the graph of f(x)=-x+1be obtained from the graph ofy=x?12)A)Shift it horizontally 1 units to the left. Reflect it across the y-axis.B)Shift it horizontally-1 units to the left. Reflect it across the x-axis.C)Shift it horizontally 1 units to the left. Reflect it across the x-axis.D)Shift it horizontally 1 units to the right. Reflect it across the x-axis.SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.13)The following graph represents the result of applying a sequence of transformations to thegraph of a basic function. Identify the basic function and describe the transformation(s).Write the equation for the given graph.13)MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Graph the function.5

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14)f(x)=x-2if x<1-3if xL114)A)B)C)D)Solve the problem.15)A retail chain sells washing machines. The retail price p(x) (in dollars) and the weekly demand xfor a particular model are related by the function p(x)=625-5x, where 50KxK500. (i) Describehow the graph of the function p can be obtained from the graph of one of the six basic functions: y=x,y=x2,y=x3,y=x, y=3x, or y=x. (ii) Sketch a graph of function p using part (i) as anaid.15)6

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A)(i) The graph of the basic function y=xisvertically expanded by a factor of 625,and shifted up 5 units.(ii)B)(i) The graph of the basic function y=xisreflected in the x-axis and verticallyexpanded by a factor of 5.(ii)7

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C)(i) The graph of the basic function y=xisvertically expanded by a factor of 5,and shifted up 625 units.(ii)D)(i) The graph of the basic function y=xisreflected in the x-axis, vertically expandedby a factor of 5, and shifted up 625 units.(ii)Graph the linear equation and determine its slope, if it exists.16)3x+5y=1116)8

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A)slope:34B)slope:34C)slope:-34D)slope:-34Find the slope and y intercept of the graph of the equation.17)y=3x-417)A)Slope=-4, y intercept=3B)Slope=3, y intercept=4C)Slope=3, y intercept=-4D)Slope=4, y intercept=39

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Provide an appropriate response.18)Use the graph to find the slope-intercept form of the equation of the line.18)A)y=-x+3B)y=x+3C)y=x-3D)y=3xFor the given function, find each of the following:(A) Intercepts(B) Vertex(C) Maximum or minimum(D) Range19)f(x)=(x+1)2-419)A)(A) x-intercepts:-3,1; y-intercept:-3(B) Vertex (1,-4)(C) Minimum:-4(D) yL-4B)(A) x-intercepts:-3,1; y-intercept:-3(B) Vertex (-1,-4)(C) Maximum:-4(D) yK-4C)(A) x-intercepts:-3,1; y-intercept:-3(B) Vertex (-1,-4)(C) Minimum:-4(D) yL-4D)(A) x-intercepts:-1,3; y-intercept:-3(B) Vertex (-1,-4)(C) Minimum:-4(D) yL-4Find the slope of the line containing the given points.20)(2,-4); (-5,8)20)A)-712B)712C)127D)-127Use interval notation to write the solution set of the inequality.21)3x+5<2921)A)(-Q,8)B)(8,Q)C)(-Q,8]D)[8,Q)10

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Provide an appropriate response.22)Use the graph to find the slope, x-intercept and y-intercept of the line.22)A)slope=-1x-intercept=(-7, 0)y-intercept=(0, 7)B)slope=1x-intercept=(0, 7)y-intercept=(-7, 0)C)slope=-1x-intercept=(7, 0)y-intercept=(0,-7)D)slope=1x-intercept=(7, 0)y-intercept=(0,-7)Solve graphically to two decimal places using a graphing calculator.23)1.3x2-2.1x-3.2>023)A)x<-0.96or x>2.57B)x<-2.57or x>0.96C)-2.57<x<0.96D)-0.96<x<2.57Solve the problem.24)The cost of manufacturing a computer part is related to the quantity produced, x, during aproduction run. When 100 parts are produced, the cost is $300. When600parts are produced, thecost is $4800. Find an equation of the line relating quantity produced to cost. Write the final answerin the form C=mx+b.24)A)C=9x-600B)C=9xC)C=9x+600D)C=600x+9For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept.25)y=4x+125)A)(i) 1(ii)14(iii)1B)(i) 1(ii)-14(iii)1C)(i) 1(ii)-4(iii)4D)(i) 1(ii)1(iii)1411

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The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial functionthat could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive?26)26)A)(i) 2(ii) NegativeB)(i) 3(ii) PositiveC)(i) 2(ii) PositiveD)(i) 3(ii) NegativeProvide an appropriate response.27)What is the maximum number of x intercepts that a polynomial of degree2can have?27)A)1B)3C)2D)Not enough information is given.For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical orhorizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y=f(x).28)f(x)=x+2x+128)12

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A)(i) x intercept: 0; y intercept: 0(ii) Domain: all real numbers except-1(iii) Vertical asymptote: x=-1; horizontal asymptote: y=1(iv)B)(i) x intercept: 0; y intercept: 0(ii) Domain: all real numbers except 1(iii) Vertical asymptote: x=1; horizontal asymptote: y=1(iv)C)(i) x intercept: 2; y intercept: 2(ii) Domain: all real numbers except 1(iii) Vertical asymptote: x=1; horizontal asymptote: y=1(iv)13

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D)(i) x intercept:-2; y intercept: 2(ii) Domain: all real numbers except-1(iii) Vertical asymptote: x=-1; horizontal asymptote: y=1(iv)Find the equation of any horizontal asymptote.29)f(x)=8x2-7x-25x2-2x+929)A)y=0B)y=72C)y=85D)NoneWrite an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure.30)30)A)f(x)=x2+5x-6B)f(x)=x2-6x+5C)f(x)=x2+5x+6D)f(x)=x2+6x+5Solve the problem.31)Financial analysts in a company that manufactures ovens arrived at the following daily costequation for manufacturing x ovens per day: C(x)=x2+4x+1800. The average cost per unit at aproduction level of x ovens per day isC(x)=C(x)/x. (i) Find the rational functionC. (ii) Sketch agraph ofC(x) for 10KxK125. (iii) For what daily production level (to the nearest integer) is theaverage cost per unit at a minimum, and what is the minimum average cost per oven (to the nearestcent)? HINT: Refer to the sketch in part (ii) and evaluateC(x) at appropriate integer values until aminimum value is found.31)14

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A)(i)C(x)=x2+4x+1800x(ii)(iii) 44 units; $185.61 per ovenB)(i)C(x)=x2+4x+1800x(ii)(iii) 22 units; $48.93 per ovenC)(i)C(x)=x2+4x+1800x(ii)(iii) 42 units; $88.86 per ovenD)(i)C(x)=x2+4x+1800x(ii)(iii) 61 units; $133.29 per ovenGraph the function.15

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