Functions Questions and Answers

Verify the following identity 1 cos 2x sin 2x tan x Which of the following three statements verifies the given equation 1 1 2 cos x 2 sin x cos x 1 cos 2x sin 2x O1 cos2x sin 2x 1 cos 2x sin 2x 1 1 2 sin x 2 sin x cos x 1 2 sin x 1 2 sin x cos x 2 cos x 2 sin x cos x 2 sin x 2 sin x cos x 2 sin x 2 sin x cos x tan x tan x tan x

Prove the given identity tan sin 0 cos 0 sec 0 Choose the correct proof below OA tan 8 sin 8 cos 0 B tan 0 sin 0 cos 0 OC tan 0 sin 0 cos 0 OD tan 0 sin 0 cos 0 sin 0 cos 0 sin 0 cos 0 sin e cos e sin e sin 0 cos 0 sin sin 0 cos 0 cos 0 sec 0 0 sin sin sin cos 0 2 2 cos cos 0 2 0 cos 0 cos 2 2 sin 0 cos 0 cos e 2 sin 0 cos 0 0 1 cos 0 cos 0 1 cos e 1 1 se sec sec sec

tan 0 cos 0 sin 0 Which of the following four statements verifies the identity OA tan 0 cos 0 sin 0 cos OC tan 0 cos 0 OB tan 0 cos 0 cos 0 sin 0 sin 0 cos sin 0 O D tan 0 cos 0 sin 0 cos 0 cos 0 sin e sin 0 cos 0 cos 0 cos 0 sin 0 sin e sin 0 cos cos 0 cos 0 sin 0 sin 0 DESK 0 sin 0 sin 0 sin 0 sin 0

3 Determine the a 0 5 equation from the graphs 10 b 5 0 5 10

y a describes direction of opening vertical stretch factor ayo azo h describes horizontal translations h 0 x h h 0 x h c describes vertical translations C70 C20 1 State the transformations a y 4 x 1 8 Order matters A value vertical stretch vertical reflection left right up down Hor K values b y x 3 5

2 Graph the following a y 3 x 4 6 b x 4 3

at 3 m s while the pipe rolls counterclockwise at w 6 rad s without slipping at B Determine the velocity of the pipe s center G G1 5 m 3 m s

a Find the inverse of the function below on the given interval and write it in the form y f x b Verify the relationships f x x and f x x f x x 36 for x 0 a f x x 36 b Verify the relationship ft x x Select the correct choice below and fill in the answer box es to complete your choice OA x x 36 Type integers or simplified fractions E x 36 36 HW Score 55 95 13 Points 0 4 of 1 x f x 36 36 Type integers or simplified fractions Verify the relationship f f x x Select the correct choice below and fill in the answer box es to complete your choice

Use the following table to determine the indicated derivatives or state that the derivative cannot be determined 6 3 0 1 4 5 f x 1 f x 2 3 a f 4 b f 1 1 C 3 7 3 2 f 3 d f 3 3 A 1 cannot be determined OB 6 8 A 4 3 Type an integer or a fraction OB 4 cannot be determined b Choose the correct answer below and if necessary fill in the answer box within your choice f 1 Type an integer or a fraction OA 3 cannot be determined 2 A c Choose the correct answer below and if necessary fill in the answer box within your choice

d 3 3x 2 2x 4x

A grocery store clerk put only packages of flour tortillas and packages of com tortillas on a shelf The ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16 Which number could be the number of packages of flour tortillas the clerk put on the shelf F G H J 23 18 14 32

Determine whether the following pair of sets is equivalent Justify your answer x x is a letter in the word cat and x x is a letter in the word scar Are the sets equivalent OA No the two sets do not have any of the same elements OB Yes the two sets consist entirely of letters OC No the two sets have a different number of elements OD Yes both sets are subsets of larger sets

Determine whether the set is well defined x x has many possessions Choose the correct answer below O not well defined O well defined

9 5x y 5 6 5 4 2 1 Ay 10 x 5y 20

Make the subject of this formula k n 12

Prove the given identity sin 0 1 cot e 1 2 Which of the following shows the key steps in proving the identity 2 2 O A sin 1 cot e sin 0 sin 0 cot 0 sin 2 OB sin 0 1 cot e sin 0 tan 0 sin 0 O c sin 0 1 cot 0 os 0 c COS COS sin 0 2 COS 0 O D sin2 0 1 cot2 0 sin 0 csc 0 sin 0 2 1 cot 0 sin 1 2 2 sec 0 0 cos cos 0 1 2 sin 0 2 sin 0 0 cos 0 1 2 sin 0 1 2 sin 0 1

Using the graph off shown below find three intervals on which f is one to one making each interval as large as possible Ay 6 3 3 A CID The intervals on which f is one to one are Simplify your answers 0 and c

Multiply and simplify sec 8 cos 0 sin 0 tan 0 sec cos 0 sin 0 tan 0 Simplify your answer

4 15 Use the Laplace transform to solve the initial value problem y y y U t 2 y 0 0 No credit for any other method

3 15 Use the Laplace transform to solve the initial value problem bo y y 1 y 0 0 y 0 0 No credit for any other method

6 1 1 Determine the slope of each line a b y 4 y f x 20 2 X y g x J 4 2 C y r X

Which of the following are causes of the increased irrationality in our society Post modernism Relativism Polarization All of the above

The extreme temperatures for each continent for a given year are listed in the data table Using a cubic model a location with a maximum temperature of 95 degrees Fahrenheit is predicted to have a minimum temperature of 86 degrees How reliable is this prediction Give at least two reasons to defend your answer Maximum Minimum F F Africa 136 11 Antarctical 59 129 Asia 129 90 Australia 128 9 Eurone 122 Continent 67

Based on a poll 63 of Internet users are more careful about personal information when using a public Wi Fi hotspot What is the probability that among three randomly selected Internet users at least one is more careful about personal information when using a public Wi Fi hotspot How is the result affected by the additional information that the survey subjects volunteered to respond The probability that at least one of them is careful about personal information is Round to three decimal places as needed h

Identify which of these types of sampling is used simple random stratified systematic or convenience 49 students are selected at random from the Saphomore class 39 from the Junior Class and 48 from the Senior Class A sample consists of every 20th student who leaves the library A pollster uses a computer to generate 500 random numbers then interviews the voters corresponding to those numbers A researcher interviews 19 work colleagues who work in his building Systematic Convenience Stratified Simple Random SP 4

1 Draw the graph of f z TOE 6 9 18 65 432 WA 9 in ON N da S 40

Question 16 Give yo V A population of bacteria is growing according to the equation P t 0 11t 1650e Use a graphing calculator to estimate when the population will exceed 3022 inc

Responded Refused 18 21 74 12 The table below summarizes results from a study of people who refused to answer survey questions If one of the subjects is randomly selected what is the probability that the selected person refused to answer Does the probability value suggest that refusals are a problem for pollsters Age 22 29 256 21 30 39 246 34 40 49 137 27 50 59 139 36 O 60 and over 203 58 The probability that a randomly selected person refused to answer is Do not round until the final answer Then round to three decimal places as needed Points 0 of 2 Save

Points 0 of 2 In a computer instant messaging survey respondents were asked to choose the most fun way to flirt and it found that P D 0 610 where D is directly in person If someone randomly selected what does P D represent and what is its value What does P D represent OA P D is the probability of randomly selecting someone who did not participate in the survey OB P D is the probability of randomly selecting someone who did not have a preference in regards to the most fun way to flirt O C P D is the probability of randomly selecting someone who does not choose a direct in person encounter as the most fun way to flirt D P D is the probability of randomly selecting someone who chooses a direct in person encounter as the most fun way to flirt

0 10 pts 3299 Write an expression of the type A log x B or A log x B for the transformed logarithmic function shown below 6 5 4 3 2 1 6 5 4 3 2 1 1 2 3 4 5 6 1 2 3 Details 4 5 16 f x Hint Use the vertical asymptote to find B To solve for A use a point on the graph and substitute the coordinates into y A log x B or y A log x B as appropriate

Draw a tree diagram for spinning Spinner A one time Use the diagram to find the number of possible outcomes Spinner A Choose the correct tree diagram below O A O C 1 O B 123 X OD

The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles A lim R lim f x Ax f x x f x Ax ni Use this definition with right endpoints to find an expression for the area under the graph of f as a limit Do not evaluate the limit f x 9x cos 9x 0 x A lim n i 1 K 2

Ten buildings are listed in the following table Find the median height of the eight tallest buildings Building Height in feet Building 1 2711 Building 2 1974 Building 3 1663 Building 4 1612 Building 5 1586 Building Building 6 Building 7 Building 8 Building Building 10 The median height of the eight tallest buildings is feet Type a whole number or decimal rounded to one decimal place as needed Height in feet 1483 1483 1478 1455 1447

0 10 pts 399 Details Starting with the graph of f x 3 write the equation of the graph that results from a reflecting f x about the x axis Y b shifting f x 4 units right Y c shifting f x 6 units upward Y

pts ILS The graph of the function f x e 4 can be obtained from the graph of g x e by one of the following actions a reflecting the graph of g x in the x axis b reflecting the graph of g x in the y axis your answer is input a or b then by one of the following actions a shifting the resulting graph to the right 4 units b shifting the resulting graph to the left 4 units c shifting the resulting graph upward 4 units d shifting the resulting graph downward 4 units Your answer is input a b c or d Is the domain of the function f x still Your answer is input Yes or No The range of the function f x is A the value of A is

A 6 00 ft tall man walks at 5 00 ft s toward a street light that is 16 0 ft above the ground At what rate is the end of the man s shadow moving when he is 6 0 ft from the base of the light Use the direction in which the distance from the street light increases as the positive direction The end of the man s shadow is moving at a rate of Round to two decimal places as needed ft s

0 4 pts 3 Details A certain disease has an incidence rate of 0 9 If the false negative rate is 4 and the false positive rate is 1 compute the probability that a person who tests positive actually has the disease Give your answer accurate to at least 3 decimal places

Select the correct location on the table Consider the following equation Which row in the table is closest to the actual solution H 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 22 3 4 2 0 9 10 2 3 17321 17889 18439 18974 19494 2 2 0494 2 0976 2 1448 2 1909 2 2361 5 2 2 2 0195 2 0385 2 0566 2 0741 2 0909 2 1071 2 1228 2 1379 2 1525 2 1567

A coffee company has found that the marginal cost in dollars per pound of the coffee it roasts is represented by the function below where x is the number of pounds of coffee roasted Find the total cost of roasting 210 lb of coffee disregarding any fixed costs C x 0 016x 7 75 for x 400 The total cost is Round to the nearest cent as needed

Select the correct answer Melissa and Robbie are flying remote control gliders The altitude of Melissa s glider h s in feet is modeled by this function where s is time in seconds after launch m 8 0 4 8 118 3181 The altitude of Robbie s glider is modeled by function r where s is time in seconds after launch Altitude feet r s 25 20 15 10 5 0 1 2 3 4 5 6 7 8 Time seconds Which glider reaches the greater maximum altitude in the first 6 seconds after launch 5 A B TS Robbie s glider Both gliders reach the same altitude on the given interval Meither glider reor imum altitude on the alven intonal

Calculate the value of x 2x 20 X 3x 10

The population P of a predator mammal depends upon the number x of a smaller animal that is its primary food source The populations of the smaller animal depends upon the amount a of a certain plant that is its primary food source If P x 3x 4 and s a 2a 2 what is the relationship between the predator mammal and the plant food source OP s a 4a 8a 8 O P s a 12a2 24a 16 P s a 6a 6 P s a 12a 12a 16 OP s a Pa

Find the domain of the composite function fog f x 10 2 g x x 1 x 2 11 x1x 21 x x 3 x x is any real number

For the given functions f x O 5 4 x 7 8 x x Find f o g x 35x 4 4 5x 4 49 35x 4 4 f and g find the requested composite function 4x 28 35x

The function f is one to one Find its inverse f x x 8x 1 Of x x Of x 7 8x 1 7x 1 7x 1 Of x x 1 8 7 Of 1 x 1 8x 1

Find the domain of the composite function fog f x g x 5x 20 x x2 4 x 1x 20 O xx is any real number xxs 4 or x 201

Evaluate the expression using the values given in the table gof 1 x 5 4 4 1 3 8 5 11 g x 5 11 12 11 1 13 O O O O 4 11 8 5

Solve a Consumers or Producers Surplus Problem A sports watch has a price demand equation given by p D z 95 2 0 027076 dollars which gives the price per watch when z watches are demanded The price supply equation for the watch is given by p S x 0 9x 2 dollars which gives the price per watch when a watches are supplied If the equilibrium quantity is 44 find the consumers surplus and the producers surplus The consumers surplus is Your answer must begin with S The producers surplus is Your answer must begin with S

Solve a Consumers or Producers Surplus Problem The supplier of a popular board game called Who Dunnit has a price supply equation given by p S x 20 2 6x dollars which gives the price per game when z games are supplied If market equilibrium is reached when 22 games are sold at a price of 77 2 eac find the producers surplus The surplus is Your answer must begin with

Use the change of base formula to compute log 5 Round your answer to the nearest thousandth