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24Chapter 1: Preparation for Calculus1.2 Linear Models and Rates of ChangeAnswer Section1.ANS:BPTS:1DIF:EasyREF: Section 1.2OBJ: Estimate the slope of a line from its graphMSC: Skill2.ANS:DPTS:1DIF:EasyREF: Section 1.2OBJ: Sketch the line passing through a point with specified slopeMSC: Skill3.ANS:BPTS:1DIF:EasyREF: Section 1.2OBJ: Calculate the slope of a line passing through two pointsMSC: Skill4.ANS:CPTS:1DIF:MedREF: Section 1.2OBJ: Calculate the slope of a line passing through two pointsMSC: Skill5.ANS:APTS:1DIF:MedREF: Section 1.2OBJ: Identify a point on a line with specified propertiesMSC: Skill6.ANS:BPTS:1DIF:EasyREF: Section 1.2OBJ: Calculate slopes in applicationsMSC: Application7.ANS:CPTS:1DIF:MedREF: Section 1.2OBJ: Calculate slopes in applicationsMSC: Application8.ANS:EPTS:1DIF:MedREF: Section 1.2OBJ: Manipulate a linear equation to determine its slopeMSC: Skill9.ANS:APTS:1DIF:MedREF: Section 1.2OBJ: Manipulate a linear equation to determine its y-interceptMSC: Skill10.ANS:BPTS:1DIF:EasyREF: Section 1.2OBJ: Write an equation of a line given a point on the line and its slopeMSC: Skill11.ANS:BPTS:1DIF:EasyREF: Section 1.2OBJ: Write an equation of a line given a point on the line and its slopeMSC: Skill12.ANS:DPTS:1DIF:EasyREF: Section 1.2OBJ: Write an equation of a line given two points on the lineMSC: Skill13.ANS:EPTS:1DIF:MedREF: Section 1.2OBJ: Write an equation of a line given two points on the lineMSC: Skill14.ANS:EPTS:1DIF:EasyREF: Section 1.2MSC: SkillOBJ: Write an equation of a line given its x- and y-intercepts15.ANS:BPTS:1DIF:MedREF: Section 1.2OBJ: Sketch the graph of a linear equationMSC: Skill16.ANS:CPTS:1DIF:MedREF: Section 1.2OBJ: Write an equation of a line given a point on the line and a line to which it isparallel/perpendicularMSC: Skill17.ANS:APTS:1DIF:MedREF: Section 1.2OBJ: Write an equation of a line given a point on the line and a line to which it isparallel/perpendicularMSC: Skill18.ANS:APTS:1DIF:MedREF: Section1.2OBJ:Write an equation of a line given a point on the line and a line to which it is perpendicularMSC: Skill19.ANS:APTS:1DIF:EasyREF: Section 1.2OBJ: Write an equation of a line given a point on the line and a line to which it is parallelMSC: Skill20.ANS:DPTS:1DIF:EasyREF: Section 1.2OBJ: Write linear equations in applicationsMSC: Application

1.2 Linear Models and Rates of Change21. ANS: DPTS: 1DIF: MedREF: Section 1.2OBJ: Write an equation of a line through the points of intersection of quadratic equationsMSC: Skill22.ANS:BPTS:1DIF:EasyREF: Section 1.2OBJ: Write linear equations in applicationsMSC: Application23.ANS:BPTS:1DIF:EasyREF: Section 1.2OBJ: Evaluate linear equations in applicationsMSC: Application24.ANS:DPTS:1DIF:MedREF: Section 1.2OBJ: Write linear equations in applicationsMSC: Application25.ANS:EPTS:1DIF:EasyREF: Section 1.2OBJ: Evaluate linear equations in applicationsMSC: Application26.ANS:CPTS:1DIF:MedREF: Section 1.2OBJ: Calculate the distance between a point and a lineMSC: Skill25

26Chapter 1: Preparation for Calculus1.3 Functions and Their GraphsMultiple ChoiceIdentify the choice that best completes the statement or answers the question.a.b.c.d.e.Evaluate (if possible) the functionat2.Evaluate (if possible) the functionat3.Evaluate (if possible) the function1. Simplify the result.–71737undefined. Simplify the result.a.b.c.d.e.at. Simplify the result.a.b.c.d.e. none of the above4.a.b.c.d.e. undefinedLet. Then simplify the expression.

1.3 Functions and Their Graphs5.Let. Evaluate the expressionand then simplify theresult.a.b.c.d.e. undefined6.Find the domain and range of the function.a. domain:range:b. domain:range:c. domain:range:d. domain:range:e. domain:range:7.Find the domain and range of the functiona. domain:range:b. domain:range:c. domain:range:d. domain:range:e. none of the above.27

28Chapter 1: Preparation for Calculus8.Find the domain and range of the functiona. domain:range:b. domain:range:c. domain:range:d. domain:range:e. domain:range:9.Evaluate the functionat10.Determine the domain and range of the function.a.b.c.d.e.a. domain:range:b. domain:range:c. domain:range:d. domain:range:e. domain:range:a. nob. yes11.Determine whether y is a function of x.

1.3 Functions and Their Graphs12.Determine whether y is a function of x.13.Use the graph of29a. nob. Yesa.given below to find the graph of the functiond.

30Chapter 1: Preparation for Calculuse.b.c.14.Use the graph ofgiven below to find the graph of the function.

1.3 Functions and Their Graphsa.d.b.e.c.31

32Chapter 1: Preparation for Calculus15.Specify a sequence of transformations for the functionwill yield the graph of h from the graph of the functiona.The functionby a vertical shiftb.e.to the left, followed byis a horizontal shiftto the left, followed byto the right.is a vertical shiftdownwards, followed by ais a vertical shiftupwards, followed by ato the right.The functionhorizontal shiftis a horizontal shiftupwards.The functionhorizontal shiftto the right, followeddownwards.The functiona horizontal shiftd.is a horizontal shiftThe functiona vertical shiftc.thatto the left.16.Given17.Determine whether the function is even, odd, or neither.and, evaluate.a.b.c.d.e.a. oddb. evenc. neither

1.3 Functions and Their Graphs18.Determine whether the function is even, odd, or neither.a. evenb. oddc. neither19.Find the coordinates of a second point on the graph of a function f if the given pointis on the graph and the function is even.a.b.c.d.e.20.Find the coordinates of a second point on the graph of a function f if the given pointis on the graph and the function is odd.a.b.c.d.e.33

34Chapter 1: Preparation for Calculus21.The horsepower H required to overcome wind drag on a certain automobile isapproximated bywhere x is the speed of the car inmiles per hour. Find. Round the numerical values in your answer to five decimal places.a.b.c.d.e.22.An open box of maximum volume is to be made from a square piece of materialcentimeters on a side by cutting equal squares from the corners and turning up the sides (see figure).Write the volume V as a function of x, the length of the corner squares.a.b.c.d.e.

1.3 Functions and Their Graphs23.An open box of maximum volume is to be made from a square piece of materialcentimeters on a side by cutting equal squares from the corners and turning up the sides(see figure).What is the domain of the ain:35

36Chapter 1: Preparation for Calculus1.3 Functions and Their GraphsAnswer J:ANS:DPTS:1DIF:Evaluate a function and simplifyANS:BPTS:1DIF:Evaluate a function and simplifyANS:CPTS:1DIF:Evaluate a function and simplifyANS:BPTS:1DIF:Simplify a difference quotientANS:APTS:1DIF:Simplify a difference quotientANS:EPTS:1DIF:Identify the domain and range of a functionANS:EPTS:1DIF:Identify the domain and range of a functionANS:BPTS:1DIF:Identify the domain and range of a functionANS:EPTS:1DIF:Evaluate a piecewise functionANS:BPTS:1DIF:Identify the domain and range of a functionANS:BPTS:1DIF:Identify equations that are functionsANS:BPTS:1DIF:Identify equations that are functionsANS:EPTS:1DIF:Graph transformations of functionsANS:APTS:1DIF:Graph transformations of functionsANS:BPTS:1DIF:Describe a transformation of an equationANS:DPTS:1DIF:Evaluate composite functionsANS:CPTS:1DIF:Identify the type of symmetry of the graph of a functionANS:APTS:1DIF:Identify the type of symmetry of the graph of a functionANS:EPTS:1DIF:Identify points on a graph using symmetryANS:BPTS:1DIF:Identify points on a graph using symmetryANS:DPTS:1DIF:Apply composite functionsANS:APTS:1DIF:Create functions in MSC:REF:MSC:REF:MSC:Section 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3SkillSection 1.3ApplicationSection 1.3Application

1.3 Functions and Their Graphs23. ANS: CPTS: 1OBJ: Identify domains in applicationsDIF:MedREF: Section 1.3MSC: Application37

38Chapter 1: Preparation for Calculus1.4 Fitting Models to DataMultiple ChoiceIdentify the choice that best completes the statement or answers the question.a.b.c.d.e.1.Determine which type of function would be most appropriate to fit the given data.exponentiallinearquadraticno relationshiptrigonometric2.Which function below would be most appropriate model for the given data?

1.4 Fitting Models to Dataa.b.c.d.no apparent relationship between x and ytrigonometricquadraticlinear3.The following ordered pairs represent temperatures in degrees Fahrenheit taken eachhour from 1:00 pm until 5:00 pm. Let T be temperature, and let t be time, wherecorrespondsto 1:00 pm,corresponds to 2:00 pm, and so on. Plot the data. Visually find a linear model forthe data and find its equation. From the visual linear model that you created, determine which of themodels that follow appears to best approximate the data.(1:00 pm ,), (2:00 pm ,), (3:00 pm ,), (4:00 pm ,), (5:00 pm ,)a.b.c.d.e.4.Each ordered pair gives the exposure index x of a carcinogenic substance and thetocancer mortality y per 100,000 people in the population. Use the modelapproximate y if. Round your answer to one decimal place.a.b.c.d.e.168.2163.6182.0172.8177.45.Hooke's Law states that the force F required to compress or stretch a spring (withinits elastic limits) is proportional to the distance d that the spring is compressed or stretched from itsoriginal length. That is,where k is a measure of the stiffness of the spring and is called thespring constant. The table shows the elongation d in centimeters of a spring when a force of Fnewtons is applied. Use the regression capabilities of a graphing utility to find a linear model for thedata. Round the numerical values in your answer to three decimal places.a.b.c.d.e.39

40Chapter 1: Preparation for Calculus6.Hooke's Law states that the force F required to compress or stretch a spring (withinits elastic limits) is proportional to the distance d that the spring is compressed or stretched from itswhere k is a measure of the stiffness of the spring and is called theoriginal length. That is,spring constant. The table shows the elongation d in centimeters of a spring when a force of Fnewtons is applied. Use a graphing utility to plot the data and graph the linear model.a.d.b.e.

1.4 Fitting Models to Datac.7.Hooke's Law states that the force F required to compress or stretch a spring (withinits elastic limits) is proportional to the distance d that the spring is compressed or stretched from itsoriginal length. That is,where k is a measure of the stiffness of the spring and is called thespring constant. The table shows the elongation d in centimeters of a spring when a force of Fnewtons is applied. Use the modelto estimate the elongation of the spring when a forceof 55 newtons is applied. Round your answer to two decimal places.a.b.c.d.e.8.08 cm6.38 cm4.68 cm2.98 cm9.78 cm8.In an experiment, students measured the speed s (in meters per second) of a fallingobject t seconds after it was released. The results are shown in the table below. Use the regressioncapabilities of a graphing utility to find a linear model for the data. Round all numerical values inyour answer to one decimal place.a.b.c.d.e.41

42Chapter 1: Preparation for Calculus9.In an experiment, students measured the speed s (in meters per second) of a fallingobject t seconds after it was released. The results are shown in the table below. Use the regressioncapabilities of a graphing utility to find a linear model for the data. Round all numerical values inyour answer to one decimal place.a.d.b.e.

1.4 Fitting Models to Datac.10.In an experiment, students measured the speed s (in meters per second) of a fallingobject t seconds after it was released. The results are shown in the table below. Use the modelto estimate the speed of the object afterseconds. Round your answer to twodecimal places.a.b.c.d.e.21.05 meters/second20.95 meters/second24.25 meters/second23.55 meters/second22.65 meters/second11.Students in a lab measured the breaking strength S (in pounds) of wood 2 inchesthick, x inches high, and 12 inches long. The results are shown in the table below. Use the regressioncapabilities of a graphing utility to fit a quadratic model to the data. Round the numerical values inyour answer to two decimal places, where applicable.a.b.c.d.e.43

44Chapter 1: Preparation for Calculus12.Students in a lab measured the breaking strength S (in pounds) of wood 2 inchesthick, x inches high, and 12 inches long. The results are shown in the table below. Use a graphingutility to plot the data and graph the quadratic model.a.d.b.e.

1.4 Fitting Models to Datac.13.Students in a lab measured the breaking strength S (in pounds) of wood 2 inchesthick, x inches high, and 12 inches long. The results are shown in the table below. Use the modelto approximate the breaking strength when. Round your answerto two decimal places.a.b.c.d.e.595.98 pounds390.19 pounds957.76 pounds801.77 pounds751.97 pounds14.A V8 car engine is coupled to a dynamometer and the horsepower y is measured atdifferent engine speeds x (in thousands of revolutions per minute). The results are shown in the tablebelow. Use the regression capabilities of a graphing utility to find a cubic model for the data. Roundthe numerical values in your answer to three decimal places, where applicable.a.b.c.d.e.45

46Chapter 1: Preparation for Calculus15.A V8 car engine is coupled to a dynamometer and the horsepower y is measured atdifferent engine speeds x (in thousands of revolutions per minute). The results are shown in the tablebelow. Use a graphing utility to plot the data and graph the cubic model.a.d.b.e.

1.4 Fitting Models to Datac.16.A V8 car engine is coupled to a dynamometer and the horsepower y is measured atdifferent engine speeds x (in thousands of revolutions per minute). The results are shown in the tablebelow. Use the modelto approximate the horsepower when theengine is running at 5500 revolutions per minute. Round your answer to two decimal places.a.b.c.d.e.260.77 hp262.73 hp262.36 hp261.38 hp261.91 hp47

48Chapter 1: Preparation for Calculus1.4 Fitting Models to DataAnswer BJ:16.OBJ:ANS:APTS:1DIF:EasyREF: Section 1.4Identify the most appropriate function for a scatter plotMSC: SkillANS:DPTS:1DIF:EasyREF: Section 1.4Identify the most appropriate function for a scatter plotMSC: SkillANS:EPTS:1DIF:EasyREF: Section 1.4Identify the best linear model for given dataMSC: ApplicationANS:DPTS:1DIF:EasyREF: Section 1.4Evaluate linear models in applicationsMSC: ApplicationANS:DPTS:1DIF:EasyREF: Section 1.4Write a linear model for data using the regression capabilities of a graphing utilityMSC: ApplicationANS:DPTS:1DIF:EasyREF: Section 1.4Plot data points and the graph of a linear modelMSC: ApplicationANS:CPTS:1DIF:EasyREF: Section 1.4Evaluate linear models in applicationsMSC: ApplicationANS:APTS:1DIF:EasyREF: Section 1.4Write a linear model for data using the regression capabilities of a graphing utilityMSC: ApplicationANS:CPTS:1DIF:EasyREF: Section 1.4Plot data points and the graph of a linear modelMSC: ApplicationANS:EPTS:1DIF:EasyREF: Section 1.4Evaluate linear models in applicationsMSC: ApplicationANS:BPTS:1DIF:MedREF: Section 1.4Write a quadratic model for data using the regression capabilities of a graphing utilityMSC: ApplicationANS:BPTS:1DIF:MedREF: Section 1.4Plot data points and the graph of a quadratic modelMSC: ApplicationANS:APTS:1DIF:MedREF: Section 1.4Evaluate quadratic models in applicationsMSC: ApplicationANS:DPTS:1DIF:MedREF: Section 1.4Evaluate cubic models in applicationsMSC: ApplicationANS:DPTS:1DIF:MedREF: Section 1.4Plot data points and the graph of a cubic modelMSC: ApplicationANS:APTS:1DIF:MedREF: Section 1.4Write a cubic model for data using the regression capabilities of a graphing utilityMSC: Application

1.5 Inverse Functions1.5 Inverse FunctionsMultiple ChoiceIdentify the choice that best completes the statement or answers the question.1.Match the graph of the function given below with the graph of its inverse function.a.d.b.e.49

50Chapter 1: Preparation for Calculusc.a.2.Match the graph of the function given below with the graph of its inverse function.d.

1.5 Inverse Functionse.b.c.false.3.The functionUse the Horizontal Line Test to determine whether the following statement is true oris one-to-one on its entire domain and therefore has an inversefunction.a. falseb. truefalse.4.The functionfunction.a. trueb. falseUse the Horizontal Line Test to determine whether the following statement is true oris one-to-one on its entire domain and therefore has an inverse51

52Chapter 1: Preparation for Calculus5.is one-to-one on its entire domain.True or False: The functiona. falseb. true6.True or False: The functionis one-to-one on the domain.a. falseb. true7.Findif8.Findif.a.b.c.d.e.a.b.c.d.e.

1.5 Inverse c.d.e.a.b.c.d.e.53

54Chapter 1: Preparation for You need 50 pounds of two commodities costing 1.80 and 2.40 per pound. Find.the inverse function of the cost functiona.b.c.d.e.

1.5 Inverse Functions5515.You need 50 pounds of two commodities costing 1.60 and 1.95 per pound.Determine the number of pounds of the less expensive commodity purchased if the total cost.a.b.c.d.e.10 pounds17 pounds7 pounds5 pounds13 pounds16.Use the functionsto find the function.a.b.c.d.e.17.Use the functions18.Evaluate the expressionto find the functiona.b.c.d.e.a. 0b.c.d.e.without using a calculator.

56Chapter 1: Preparation for Calculus19.Evaluate the expressionwithout using a calculator.20.Evaluate the expressionwithout using a calculator.21.Write the following expression in algebraic form.22.Write the following expression in algebraic form.a.b.c.d.e.a.b.c. 3d. 5e. 4a.b.c.d.e.a.b.c.d.e.

1.5 Inverse Functions23.Write the following expression in algebraic form.24.Solve the following equation for .a.b.c.d.e.a.b.c.d.e.57

58Chapter 1: Preparation for Calculus25.a.b.c.d.e.Solve the following equation for .

1.5 Inverse Functions1.5 Inverse FunctionsAnswer J:ANS:APTS:1DIF:EasyIdentify the graph of the inverse of a functionANS:CPTS:1DIF:EasyIdentify the graph of the inverse of a functionANS:BPTS:1DIF:MedRecognize invertible functionsANS:APTS:1DIF:MedRecognize invertible functionsANS:BPTS:1DIF:MedRecognize invertible functionsANS:BPTS:1DIF:MedRecognize invertible functionsANS:EPTS:1DIF:EasyConstruct the inverse of a fun

Calculus Hybrid Early Transcendental Functions 6th Edition Larson Test Bank . Identify the choice that best completes the statement or answers the question. _ 1. Estimate the slope of the line from the graph. a. b. 5 . Calculus Hybrid Early Trans