Functions Questions and Answers

1 point a Consider the relation R on the set A X Y Z defined by R X Y X Z Y X Y Z Z X Z Y This relation is not reflexive What element s would we need to add to R in order for it to be reflexive b Consider the relation R on the set A X Y Z defined by R X X X Y X Z Y Y Y Z Z X This relation is not symmetric What element s would we need to add to R in order for it to be symmetric c Consider the relation R on the set A X Y Z defined by R X Y Y X Z Z This relation is not transitive What element s would we need to add to R in order for it to be transitive

1 point Consider the relations R R2 R3 R R5 on A 1 2 3 4 defined by R 1 2 2 1 R 2 2 2 3 2 4 3 2 3 3 3 4 R3 1 1 1 2 2 1 2 2 3 3 4 4 R4 1 2 2 3 3 4 R5 1 1 2 2 3 3 4 4 Determine which of the following statements are true Select all that apply A R is not symmetric B R is reflexive C R is symmetric D R4 is transitive E R is reflexive F R5 is transitive G R5 is not reflexive H R3 is reflexive I R is transitive J R3 is not transitive K R4 is symmetric L None of the above

1 point Determine whether each of the relations whose digraphs are given below are reflexive symmetric transitive or none of the above Select all that apply a A Reflexive OB Symmetric C Transitive b 0000 c 0000 d A D None of the above 200 A A Reflexive B Symmetric C Transitive D None of the above A D A Reflexive B Symmetric C Transitive D None of the above A D A Reflexive OB Symmetric 20 C Transitive D None of the above A D A Reflexive OB Symmetric C Transitive Co B E C B E B B C B

1 point Consider the relations R R2 R3 R4 R5 on A 1 2 3 4 defined by R 1 2 2 1 R 2 2 2 3 2 4 3 2 3 3 3 4 R3 1 1 1 2 2 1 2 2 3 3 4 4 R4 1 2 2 3 3 4 R5 1 1 2 2 3 3 4 4 Determine which of the following statements are true Select all that apply A R is not symmetric B R is reflexive C R is symmetric D R4 is transitive E R is reflexive F R5 is transitive G R5 is not reflexive H R3 is reflexive I R is transitive J R3 is not transitive K R4 is symmetric L None of the above

1 point Let A denote the set of all people Determine whether each of the relations on A given below are reflexive symmetric transitive or none of the above Select all that apply a a is older than b A Reflexive B Symmetric C Transitive D None of the above b a and b have a common child A Reflexive B Symmetric C Transitive D None of the above c a and b were born on the same day A Reflexive B Symmetric C Transitive D None of the above d a has the same first name as b A Reflexive B Symmetric C Transitive D None of the above

14 Given two sets A and B which one of the following is equivalent to AUB OA B 0 0 O An B OB A

3 Let S be a set and n be an integer If P S 2 then S is

10 Which one of the following statements is false O 2 EAUB implies that if 2 E A then 2 B 1 2 C A implies that 1 A and 2 A 2 C A B and 1 C B implies that 1 2 CAU B 1 2 CAN B implies that 1 2 CA and 1 2 CB

7 Given a set A of 0 elements what is the number of elements in P A

4 The members of the set S n n is the square of an integer and 0 n 40 is O 0 1 2 3 4 5 6 O 1 4 9 16 25 36 O 1 2 3 4 5 6 0 1 4 9 16 25 36

A new sidewalk will be 6 feet wide 220 feet long and filled to a depth of 6 inches 0 5 foot with concrete How many cubic yards of concrete are needed The new sidewalk needs 24 4 cubic yards of concrete Round to one decimal place as needed C

typical glass of wine contains about 19 grams of alcohol Consider a 105 pound woman with approximately 4 liters 4000 milliliters of blood who drinks two glasses of wine Complete parts a nd b below a If all the alcohol were immediately absorbed into her bloodstream what would her blood alcohol content be 9 100 mL Round to two decimal places as needed Note that a blood alcohol content BAC of 0 08g 100mL is the legal driving limit in the U S A BAC at or above 0 4g 100mL usually leads to coma or death Explain why it is fortunate that in reality the alcohol is not absorbed immediately Choose the correct answer below OA It is fortunate that alcohol is not absorbed immediately because this blood alcohol content is above the legal limit for driving and is a dangerous level of intoxication OB It is fortunate that alcohol is not absorbed immediately because although this blood alcohol content is below the legal limit it will impair brain function OC It is fortunate that alcohol is not absorbed immediately because this is a lethal concentration of alcohol and is far beyond the legal limit OD It is fortunate because any amount of alcohol consumption can impair brain function b Again assume all the alcohol is absorbed immediately but now assume her body eliminates the alcohol through metabolism at a rate of 11 grams per hour What is her blood alcohol content 3 hours after drinking the wine 100 mL Round to two decimal places as needed Is it safe for her to drive at this time Explain plophol content is lower than it was three hours ago

For the following situation find the average monthly expense that you would use in budgeting for the given expense Note Annual means once a year and semiannual means twice a year You own your own home and pay 1600 annually in homeowners insurance 2500 semiannually in property tax and 850 monthly in mortgage house loan payments In addition just to be safe you decide to set aside 1760 per year for unexpected expenses for example water heater replacement sewer clean out or roof repair The average monthly expense that you would use in budgeting is

G A report on the trends in college pricing in a certain year included the information in the accompanying relative frequency distributions for public and private nonprofit four year college students Tuition and Fees 3 000 to 6 000 6 000 to 9 000 9 000 to 12 000 12 000 to 15 000 Proportion of Students Relative Frequency Private Nonprofit Four Year College Students Public Four Year College Students 0 04 0 40 0 26 0 13 0 04 0 04 0 02 0 02 0 02 0 02 15 000 to 18 000 18 000 to 21 000 21 000 to 24 000 24 000 to 27 000 27 000 to 30 000 30 000 to 33 000 33 000 to 36 000 36 000 to 39 000 39 000 to 42 000 42 000 to 45 000 45 000 to 48 000 a Construct a relative frequency histogram for tuition and fees for students at public four year colleges Wr center and variability 0 01 0 00 Chapter 0 00 0 00 0 00 0 02 0 06 0 02 0 02 0 03 0 03 0 04 0 07 0 09 0 09 0 09 0 08 0 07 0 07 0 22 G a few sentences describing the distribution of tuition and fees commenting on shape The center is in the range Select B Values are spread from a low range of

Using synthetic division determine whether the numbers are zeros of the polynomial function 2 x 7x 11x 20 5 2 f x 2x Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The number 5 is not a zero of the polynomial function because f 5 of the polynomial function because f 2 and the number 2 is a zero OB The number 5 is a zero of the polynomial function because f 5 and the number 2 is not a zero of the polynomial function because f 2

Using examples show how to convert among the Fahrenheit Celsius and Kelvin temperature scales Choose the correct answer below C O A Conversion between Celsius Fahrenheit and Kelvin can be done using conversion formulas So to convert 60 F to Celsius and Kelvin use the formulas C 1 8F 32 to convert to Celsiu and the then use K C 273 15 to convert to Kelvin to get 60 F 76 C 349 15K OB Conversion between Celsius Fahrenheit and Kelvin can be done using conversion formulas So to convert 60 F to Celsius and Kelvin use the formulas C 1 8F 32 to convert to Celsiu and then use K C 273 15 to convert to Kelvin to get 60 F 140 C 413 15K OC Conversion between Celsius Fahrenheit and Kelvin can be done using conversion formulas So to convert 60 F to Kelvin and Celsius use the formulas K F 273 15 to convert to Kelvi and then use C K 32 1 8 to convert to Celsius to get 60 F 333 15K 167 31 C O D Conversion between Celsius Fahrenheit and Kelvin can be done using conversion formulas So to convert 60 F to Celsius and Kelvin use the formulas C and then use K C 273 15 to convert to Kelvin to get 60 F 15 56 C 288 71K F 32 1 8 to convert to Celsius

If your car gets 29 miles per gallon how much does it cost to drive 370 miles when gasoline costs 3 00 per gallon The cost is Simplify your answer Round to the nearest cent as needed

A new sidewalk will be 6 feet wide 220 feet long and filled to a depth of 6 inches 0 5 foot with concrete How many cubic yards of concrete are nee The new sidewalk needs cubic yards of concrete Round to one decimal place as needed COD I

If you sleep an average of 7 4 hours each night how many hours do you sleep in a year Assume that this year is a non leap year You sleep hours in a year Type an integer or a decimal

Coffee The National Coffee Association reported that 64 of U S adults drink coffee daily A random sample of 225 U S adults is selected Round you answers to at least four decimal places as needed Part 1 of 6 a Find the mean H P The mean is 64 Alternate Answer The mean Part 1 6 Part 2 of 6 is 0 64 b Find the standard deviation d P The standard deviation an is

HQ Four Quadrant Ordered Pairs B C 3 3 G E C Z 4 3 2 4 S Write the ordered pair for each given point 8 4 9 W 11 I 10 12 Z 2 2 2 1 1 2 4 4 5 8 Tell what point is located at each ordered pair 1 3 7 3 6 4 2 8 7 4 9 7 8 9 5 8 9 6 3 8 13 G 14 T Plot the following points on the coordinate grid 17 O 7 4 19 V 2 5 18 F 3 6 20 A 2 9 W X messa 21 Y 1 6 22 U 2 5 1 2 6 1 D 7 4 4 8 1 3 15 D 8 6 16 J 3 1 23 M 1 5 24 N 8 8

Use a standard normal distribution table to find the percent of the total area under the standard normal curve between the following z scores z 0 8 and z 1 Click the icon to view the standard normal distribution table The percent of the total area between z 0 8 and z 1 is Round to the nearest integer

Click the icon to view the area under the standard normal curve table What problem solving method should be used OA The Analogies Principle B Draw Pictures OC Relate a New Problem to an Older One OD Be Systematic The area under the standard normal curve from 0 to 2 00 is Round to four decimal places as 0 Normal Curve Areas 79 Z 1 2 3 45 0 00 0000 0398 0793 1179 1554 1915 2257 2580 2881 3159 3413 3643 3849 4032 4192 4332 4452 4554 4641 4713 4772 4821 4861 z 01 0040 0832 1217 1591 1950 2291 2611 2910 3186 3438 3665 3869 4049 4207 4345 4463 4564 4649 4719 4778 4826 4864 02 0080 0478 0871 1255 1628 1985 2324 2642 2939 3212 3461 3686 3888 4066 4222 4357 4474 4573 4656 4726 4783 4830 4868 03 0120 0517 0910 1293 1664 POIO 2019 2357 2673 2967 3238 3485 3708 3907 4082 4236 4370 4484 4582 4664 4732 4788 4834 4871 04 0160 0557 0948 1331 1700 2054 2389 2704 2995 3264 3508 3729 3925 4099 4251 4382 4495 4591 4671 4738 4793 4838 4875 1 05 0199 0596 0987 1368 1736 2088 2422 2734 3289 3531 3749 3944 4115 4265 4394 06 0239 0636 1026 1406 1772 2123 4608 4686 4750 4803 4846 4881 07 0279 0675 1064 1443 1808 2157 4525 4616 08 0319 0714 1103 1480 1844 2190 2517 3599 3810 3997 4162 4306 4429 4535 4625 4699 4761 4812 4854 4887 09 0359 0753 1141 1517 1879 2224 2549 2852 3133 3389 3621 3830 4015 4177 4319 4441 4545 4633 4706 4767 4817 4857 4890

In a road worthiness test on 240 cars 60 passed The number that failed had faults in Clutch Brakes and Steering as follows Clutch only 28 Clutch and Steering 14 Clutch Steering and Brakes 8 Clutch and Brakes 20 Brakes and Steering only 6 The numbers of cars with faults in Steering only is twice the number of cars with faults in Brakes only a Draw a Venn diagram to illustrate this information b How many cars had i faulty Brakes ii only one fault

a Sketch the curves y x 1 and y 7 x on the same axes Find the area enclosed between the curves b

2 of the function f x 2x 37 12x 4 using the second derivative and sketch the graph

Using LEIBNIE S RULL find the 4th derivative U 3x 4xt Wxes10

Let S T be sets in a universe U and let x y U a Use the definition of set subtraction to complete the following statement ES T if and only QA ES and x T OB x S and x E T OC ES or x T OD x Sorr ET OE None of the above b Use the negation of the previous answer to finish the following statement x S T if and only OA ES or x T OB x S and x T OC x Sor x E T OD ES and x T OE None of the above

Question Owners of a bike rental company that charges customers between 5 and 25 per day have determined that the number of bikes rented per da can be modeled by the linear function n p 450 18p where p is the daily rental charg How much should the company charge each custom per day to maximize revenue Do not include units c dollar sign in your answer

Len Use a transformation of the graph of y to graph the function h z 6 x 1 3 29 9 9 X 122 9 X

Solve the abs 1 42 11 2 The smaller solution is fraction symbol A Type an integer or a simplified fraction Use the slash key as a The larger solution is on symbol A Type an integer or a simplified fraction Use the slash key as a

Graph the y 4 3 x 2

State the domain range for each of the following relations and if it is a function or not a 2 1 1 0 0 1 1 0 2 1 b 2 1 1 0 0 1 1 0 2 1 c 5 2 00 3 MM d e 5

a 2 1 1 0 0 1 1 0 2 1 c f X Y 00 2 WONS following relations and if it is a function or not b 2 1 1 0 0 1 1 0 2 1 d g MA e h

Directions Find the zeros of the functions below by factoring 1 f x x 5x 6x 3 f x x 17x 16 5 f x 6x 7x 5x 7 f x 4x 5x 1 9 f x 4x 16x 25x 100 2 f x 2x 22x 56x 4 f x 2x 5x 7x 6 f x 3x 13x 4x 8 f x 4x 80x 204x 10 f x 3x x 12x 4

Question A bike rental company charges its customers p dollars per day to rent a bike where 5 p 30 The number of bikes rented per day can be modeled by the linear function n p 600 20p How much should the company charge each customer per day to maximize revenue Do not include units or a dollar sign in your answer Provide your answer below

Two functions g and fare defined in the figure below 2 5 7 a Domain of g 09 Range of g 8 Domain of f 3 Range of f Find the domain and range of the composition fog Write your answers in set notatic a Domain of fog 0 b Range of fog 0 X 0 0

Suppose you own a savings bond that will pay you 100 in 7 years If the annual interest rate is 2 what is the present value of the savings bond O 27 91 O 87 06 93 64

represents a function a set of ordered pairs or hain and range of the 8 For each relation below Determine whether the relation is a function Justify your answer Identify the domain and range relation of each a 1 1 2 8 3 27 4 64 b 3 4 3 5 3 6 3 7 d Does the set of ordered pai function Explain b Suppose the elements in th were reversed Use the asso number of sides Would t a function Explain c Identify the domain and relation in parts a and b 11 The Rassemblement jeunes

of d de 6 Write in function notation a C 20n 8 b P n 3 c t 5d d y x 3 2 3

1 Evaluate the following expressions given the functions below h x 12 X g x 3x 1 a g 10 b f 3 c h 2 d j 7 e h 3 f g 5 g f 4 f x x 7 h Find x if g x 16 i Find x if h x 2 i Find x if f x 23 j x 2x 9

Is life so dear or peace so sweet as to be purchased at the price of chains and slavery Forbid it Almighty God I know not what course others may take but as for me give me liberty or give me death Patrick Henry William Jennings Bryan argued that Patrick Henry s words applied to which of the following O United States citizens O United States citizens living abroad United States citizens and all foreign people OForeigners living and working on United States soil

Two functions g and fare defined in the figure below w b Domain of g 19 Range of g Domain of Range of f Find the domain and range of the composition fog Write your answers in set notatio a Domain of fog 0 Range of fog X 0 0

The functions f g and h are defined as follows f x 7 4x 8 x 3 x h x 6 5x Find s 8 3 and h 4 Simplify your answers as much as possible 0 h 4 olo X 5

Domain Range Function Not a function Relation 1 Function Not a function t r d N k z a N N N Relation 3 2 8 7 7 8 7 9 8 Domain Range 0 door 7 lake 5 5 4 Function Not a function Relation 2 Function Not a function cloud lake door Relation 4 k 0 b 0 t 0 w 0

Suppose that the functions q and r are defined as follows q x x 2 r x x 2 Find the following 9 r 4 rog 4 X 6

point 3 possible Determine the number of ways to perform the task described Eight players are to be selected from a 24 player baseball team to visit schools to support a summer reading program In how many ways can this selection be made There are different ways 8 players can be selected from a 24 player baseball team Simplify your answer Type a whole number

14 For the function f x 5x 11 determine stasangat 01 a f 1 c f 0 ow 6 is b f 3 d f 1 2 18 tedt fert

9 For each a tab ble of values below i Explain why the relation is a function ii Identify the independent variable and the dependent variable Justify your choices iii Write the domain and Number of Cans of Juice Purchased n 1 2 3 4 range Cost C 2 39 4 00 6 39 8 00 id 15

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