Functions Questions and Answers

1000 900 800 a range 700 600 Amount 500 of flour grams 400 300 100 Time minutes Write your answers as inequalities using x or y as appropriate Or you may instead click on Empty set or All reals as the answ h demain 0 0 0 0 Oso 8 08 20 Empty set a reals

The plot below represents the function f x Y 2 ex 2 3 2 72375 3 Evaluate f 1 f 1 MAY bient TAMAN Mari www www wwwww HALK INTEN

3 40 Use nodal analysis to find V in the circuit in Fig P3 40 6 kn V 6 kn Figure P3 40 6 kn 12 V 6 kN 6 kn

Josh is exploring the formula for the circumference of a circle He computed the circumferences of several circles wit different radii He then plotted the results and connected them with a line as shown below The graph shows the circumference in mm versus the radius in mm Find the domain and the range of the function shown Circumference mm 150 a domain 135 120 105 90 75 60 45 30 15 36 Radius mm Write your answers as inequalities using x or y as appropriate Or you may instead click on Empty set or All reals as the answer X 030 O OSO 08

5 4 w 2 1 sfx 3 H 13 1 2 a Is g 1 negative Yes No 3 5 b For which value s of x is g x 0 Write your answer using interval notation 0 c For which value s of x is g x 0 If there is more than one value separate them with commas

rse Packet on the domain of a function Functions Course Packet on functions domain and range Determine the domain of each of the following functions Enter your answer using interval notation a Domain of x 8x 15 b Domain of c Domain of d Domain of 19 x x 8x 15 19 X x 8x 15 19 X 2 8x 15

Complete the following for the system of equations 4x Sy 7 0 8x 1 6y 1 4 a Use a graphing utility to graph the equations in the system y 10t

Solve the system of linear equations Enter your answers as a comma separated list If there is no solution enter NO SOLUTION IF the system has an infinite number of solutions set x3 t and solve for X and x in terms of t 3x1 2x2 4x3 5 x1 x 2x3 6 2x13x2 6x3 9 X1 X2 X3

Some 4 5 7 questions supply a data set like the one below which must be used in order to answer the question 8 9 D 2 7 5 8 You can copy the data set into another program such as a spreadsheet or a statistical software program to perform calculations with the numbers in the given c Click the icon to view instructions for copying a data set into another program The result 9 8 of 9 points H dding Points 0 of 1 Add the numbers in the data set either by hand or by using the Click to copy table icon to copy the data into a program which can perform the calculation for

The following table contains order dependent setup times for three jobs Following Job s Setup Time hrs A Preceding Job B C Setup Time hrs 2 4 3 2 2 0 A Al B C 1 8 2 2 1 4 0 8 2 6 1 3 Click here for the Excel Data File Which processing sequence will minimize the total setup time

Identify the following users as either External users or Internal users a Business press b District attorney c Shareholders d Lenders e FBI and IRS f Consumer group g Creditors h Regulators i Managers j Nonprofit donor k Distribution managers 1 External auditors

A process that produces computer chips has a mean of 04 defective chips and a standard deviation of 003 chips The allowable variation is from 038 to 042 defective a Compute the capability index Cp for the process Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places Capability Index b Is the process capable Hint Use 1 33 as the standard capabality index O No Yer

The table shows the position of a motorcyclist after accelerating from rest t seconds s feet 0 4 9 10 6 23 1 i 2 4 ii 3 4 iii 4 5 iv 4 6 a Find the average velocity in ft s for each time period ft s flo ft s ft s 0 ft s 1 2 3 4 5 6 50 3 109 3 237 6 b Plot the points in the table to create a graph of s as a function of t to estimate the instantaneous velocity in ft s whe

A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant August usage was forecasted to be 53 percent of capacity actual usage was 52 percent of capacity A smoothing constant of 05 is used a Prepare a forecast for September Round your final answer to 2 decimal places Forecast for September percent of capacity b Assuming actual September usage of 60 percent prepare a forecast for October usage Round your answer to 2 decimal places

d 4 d 0 4 L Domain Range y intercept Asymptote Interval of increase decrease e 2 Domain Range y intercept Asymptote Interval of increase decrease Domain Range y intercept Asymptote Interval of increase decrease

Identify the information from the equation 1 Given the equation y 8 i Does this equation represent growth or decay ii What is the growth or decay factor iii What is the initial value iv What is the domain x v What is the range

3 Given the equation y 5 7 5 Does this equation represent growth or decay ii What is the growth or decay factor iii What is the initial value iv What is the domain v What is the range 4 Given the equation y 100 1 1 Does this equation represent growth or decay ii What is the growth or decay factor iii What is the initial value iv What is the domain v What is the range

At the beginning of April a colony of ants has a population of 5 000 A scientist noticed that the colony population was decreasing each month to 80 of the previous month s population 2 3 4 Number of Months 5 0 1 2 3 1 Is the ant colony population an example of exponential growth or decay Explain Expontential Decay because it is decreasing What is an equation that models the ant colony population a m months after it is first measured What is the domain and range of this function Complete the following statement As the months increase the ant colony population Ant Colony Population 5000 Estimate the ant colony population on month 1 5 Show your work 4000 3200 2560

Refer to the figure below relating to a commercial printer customer and the company that supplies the paper Technical requirements Importance to customer Customer requirements Paper will not tear 3 Consistent finish No ink bleed Prints cleanly 1 Paper width 2 3 Paper thickness Roll roundness 7 Coating thickness Tensile strength Paper width Paper thickness ORoll roundness A Coating thickness Tensile strength Paper color a What technical requirements have the highest impact on the customer requirement that the paper not tear You may select more than one answer Click the box with a check mark for the correct answer and click to empty the box for the wrong answer ololo Relationships Strong 9 Medium 3 Small 1

A construction crew is lengthening a road Let L be the total length of the road in miles Let D be the number of days the crew has worked Sup that L 4D 300 gives L as a function of D The crew can work for at most 80 days Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of valu Domain Range Description of Values Onumber of days the crew has worked Olength of the road in miles Onumber of days the crew has worked Olength of the road in miles Set of Values Choose one Choose one

A manager must make a decision on shipping There are two shippers A and B Both offer a two day rate A for 530 and B for 521 In addition A offers a three day rate of 466 and a nine day rate of 417 and B offers a four day rate of 459 and a seven day rate of 432 Annual holding costs are 37 percent of unit price Three hundred and twenty boxes are to be shipped and each box has a price of 154 Which shipping alternative would you recommend Round your intermediate calculations to 3 decimal places and final answers to 2 decimal places Option 2 days 3 days 9 days A Cost ship two day using A O ship three day using A O ship seven day using B O ship four day using B Oship two day using B Option 2 days 4 days 7 days B Cost

The forecast for each week of a four week schedule is 50 units The MPS rule is to schedule production if the projected on hand inventory would be negative without it Customer orders committed are follows Customer Order 52 35 Week 21234 538E 2582 20 12 Use a production lot size of 75 units and no beginning inventory Determine the available to promise ATP quantities for each period Leave no cells blank be certain to enter 0 wherever required

1 Show that the inverse of an increasing function is increasing and the inverse of a decreasing function is decreasing 2 Find the functions f and g such that f g is even and f g is odd 3 f R a R b and f x is one to one and onto f x given What is the if x 1 x 3 if x 1 is given Find the value of a for the continuity of f x at x 1 4 f x 5 f x 2x a X x 4 is given Sketch the graph of f x 2x 11 3x 4 is

A vehicle factory manufactures cars The unit cost C the cost in dollars to make each car depends on the number of cars made If x cars are made then the unit cost is given by the function C x 0 8x 256x 36 963 What is the minimum unit cost Do not round your answer

hat range of P 1 would alternative A be the best choice if the goal is to maximize expected profit ose Alternative A if P 1 is less than 0 361 greater than 0 361 less than 25 greater than 25

For the scenario given determine the smallest set of numbers for its possible values and classify the values as either discrete or continuous the number of presidents in U S history Choose the smallest set of numbers to represent the possible values integers irrational numbers natural numbers Orational numbers Oreal numbers whole numbers Are the values continuous or discrete O continuous

For the scenario given determine the smallest set of numbers for its possible values and classify the values as either discrete or continuos the fuel efficiency in miles per gallon for a fleet of rental cars Choose the smallest set of numbers to represent the possible values O integers O irrational numbers natural numbers Orational numbers Oreal numbers Owhole numbers Are the values continuous or discrete continu

Choose the correct number line for the number being plotted 10 30 4 3 2 1 1 2 3 4 5 6 3 2 1 0 1 2 3 4 5 6

Write each polynomial in completely factored form One factor is given Find all the x intercepts zeros the y intercept then sketch the graph without a graphing calculato 1 f x x 9x 23x 15 x 5 2 f x x x 14x 24 x 3 94 SS

Determine the distance between the two given numbers Simplify your answer completely 6 and 13

Choose the correct number line for the number being plotted 1 6 0 1 0 2 0 3 0 4 0 5 0 0 1 0 2 0 3 0 4 0 5

Write the slope intercept form of the equation of each line given the slope and y intercept 11 Slope 1 y intercept 2 x 1x 2 13 Slope 3 y intercept 2 x 3x 2 1 15 Slope y intercept 1 2 Y X 1 17 Slope 7 y intercept 2 Y 7x 2 Sketch the graph of each line 19 y x 4 21 y 4x 5 10 5 3 4 3 5 4 3 2 1 0 A 3 2 12 Slope 13 y intercept 3 3x 3 32 14 Slope 4 16 Slope DIMIN 18 Slope y intercept 1 4 x 1 5 2X G y intercept 4 4 3 1 y intercept 0 20 y 5x 1 4 3 X 4 22 y x 5 4

Solve the inequality Write the solution set in interval notation Simplify your answer completely 12 3x 11 13 3 Graph the inequality Use the tools to enter your answer 4 10 on Co 10

Graph the equation using any method y 2x 1 O No Solution 5

Question 2 Suppose that in a two commodity world the consumer s utility function takes the form 1 p u x x a a x This utility function is known as the constant elasticity of substitution CES utility function 1 Show that the CES utility function is homothetic 2 Show that as p 0 for every pair 2 22 the marginal rate of substitution between goods 1 and 2 converges to the MRS of the generalized Cobb Douglas utility function 3 Show that as p for every pair the marginal rate of substitution be tween goods 1 and 2 converges to the MRS of the Leontief utility function

There were 104 females and 78 males present at the high school pep rally Find the ratio of males to the total number of people present Express as a simplified ratio 7 3 3 4 3 7 4 3

Consider the following system of equations and its graph 2x y 4 16 4r 2y 6 Y 201 8 Go 6 4 2 20 L 8 10 LEY St 2z y 4 so A What is the solution of the system Answer z y 8 in the boxes below enter either the letter A or B to match the equation to the graph sho a Graph A

Find the domain and range of the function graphed below 5 4 3 2 Domain 2 1

What is the domain of the function in the graph 20 n 18 16 14 12 10 8 649 2 00 n 8 08 p 16 08 n 16 8 Es

156 A 6 f x 3 9x 2 g x 1 x 2 4 TROCA 9 B 10 C 18 1 9 2 G fog 2 4y 2 x D 28 E 38

d For the following Boolean expression give F a b c d a b d c b a c d i The truth table ii The Karnaugh map iii The minimal sum of products expression

For the following pair of functions find a f g x b f g b c f g x and d g f x f x 5x 3x 3 g x x 5x 3 a f g x x 3x 3 bl iftalb

a Let f and g be two functions defined from R R with f 1 1 a g x x 1 Find gof 1 gof 2 and gof z

d Let f R 1 R with f x 5x 3 x 1 i What is the image of f ii Find d E R such that the function f R 1 R d is a bijection Explain your answer iii Construct the inverse function of f

36 ASE 1 2 3 4 11 10 x x A 10 66 B 11 1 P C 12 D 11 212 ASLAN H E 12

Determine whether this table represents a probability distribution P x X 0 1 3 4 0 23 0 09 0 15 0 83 Yes because P x is 100 No because x 0 No because P x has negative No because x has negative No because P x is not 100

1 46 Spencer Company has a 220 petty cash fund At the end of the first month the accumulated receipts represent 45 for delivery expenses 135 for merchandise inventory and 14 for miscellaneous expenses The fund has a balance of 26 The journal entry to record the reimbursement of the account includes a Multiple Choice Debit to Petty Cash for 220 Credit to Cash Over and Short for 26 Debit to Cash Over and Short for 26 Credit to Cash for 194 to Inventory for 135

33 How many O s are there at the end of 401 681 19

EX 4 vehicles and t is measured in minutes 0 t 30 A Find V t for t 18 V t 92 15 sin 6 96 19 100 75 60 25 B Make a sketch of the graph of time vs number of vehicles Be sure your graph has a scale C What is the average rate of change of the vehicles at the departing flights over the time interval 15 t 20 Indicate units of measure V t 92 15 sin where V t is measured in AROC 92 Time Interval 18 18 1 18 18 01 18 18 001 15 20 20 15 4 D Estimate the instantaneous rate of change of vehicles at t 18 by finding the average rates from t 18 to t 18 1 t 18 to t 18 01 and t 18 to t 18 001 34567 Average Velocity 4 8252 4 8032 4 8010 SEN 8 9 10 92 15sin E Why can t the instantaneous rate of change of traffic in the departure lane with respect to time he calculated using the method in part 2

The total daily cost in dollars of producing x park benches is given by C x 2250 15x 0 1x A Sketch the graphs of the average cost function and the marginal cost function on the same set of coordinate axes B Find the minimum average cost A Choose the correct graph below OB OA 200 100 0 0 100 200 B The minimum average cost is 200 100 0 100 200 O C 200 100 of 0 100 200 D 200 100 04 0 100 200 5