Functions Questions and Answers

a The unit circle is the circle centered at b The equation of the unit circle is c Suppose the point P x y is on the unit circle Find the missing coordinate 1 P 1 11 P P 1 iv p 1 with radius 1

O Determine the equation for the sinusoidal function below You may choose to state your answer as either a sine or cosine function 4 marks 5 3 AN 14 V 1200 20 240 0

If f x 5x 7 then O O O O x x 7 5 f x x 7 f x 7x 5 r

Which type of relation is represented by the data below X 1 2 3 4 5 6 7 y 2 6 12 20 30 42 56 None of the above Linear Exponential Quadratic

Part 1 You may use a scientific calculator for this part no graphing capabilities 3 Sketch the graph of an example of a single function f that satisfies all of the following conditions worth 6 points lim f x 7 lim f x 4 f 3 6 lim f x o lim f x lim x 1 x 3 x 4 X 8 6 3 6 5 34 4 24 34 4 54

Find the reference angle for radians 8 5 010

Find the reference angle for 0 radians 13T 15 3 B JU

A drug trial had 226 participants A survey was done to gather information about the participants experiences with side effects The table below gives the results for two possible side effects Had anxiety but not drowsiness Had drowsiness but not anxiety Had anxiety or drowsiness or both Construct a Venn diagram illustrating these results Then answer the questions All participants in the survey Had anxiety 0 Number of participants 15 126 141 7 These buttons change the Venn diagram Had drowsiness 0 How many participants had drowsiness participants How many participants had both anxiety and drowsiness participants X

Using the table write the given Egyptian numeral as a Hindu Arabic numeral 1000 1 11 100 AAA 10 000 PARAOOOOnnnn 100 000 1 000 000 Type an integer 9999nnnn c

Watch help video Select the expression that is equivalent to 1 1 7x 2 1 7x 1 O 7x 7m 2 Submit Answer

Consider the two functions y x 3 and y2 b on the interval a a if a 7 5 What value does b have to be in order for the area between y and y2 and a a to equal 52 8 Round your answer to five decimal places 202

2 Using the graph of f x and the definition of continuity a Is the function continuous at x 0 Why or why not b Is the function continuous at x 2 Why or why not c Is the function continuous at x 6 Why or why not f x 35

d lim 5 h 9 5 h 6 5 9 5 6 h 0 h 4x 17 x 3 x 3 e lim

erform each mathematical function indicated reduce each answer to the lowest possible terms and change any improper fraction to a mixed number 1 1 8 4 7 2 79 7 18 32 7 77 78 18 32 9 3 3 1 18 2 3 3 18

Use the ALEKS calculator to evaluate each expression Round your answers to the nearest hundredth If applicable click on Undefined For each expression make sure you are in the correct calculator mode sec 9T 11 cot 300 csc 2T 0 7 Undefined X

length of a shadow of a building is 71 ft when the sun is 67 above the horizon Find the height of the building Round your answer to the nearest tenth 7

A kite is flying 75 ft off the ground and its string is pulled taut The angle of elevation of the kite is 59 Find the length of the string Round your answer to the nearest tenth B 75 59 A

3x 3 2 x 3 Multiply both sides of the equation by the denominator of the fraction 3 x EXE 3 3 2 2 Simplify both sides of the equation 3x 3 2 2 x 6 Solve for x x 9 Move the x terms to one side of the equation and the constants to the other side 1 x 9 9 12 Step 2 Check Substitute your answer from part 1 into the original equation 3 22 3 6 Simplify and see if the equality holds 2

What value s of y will make the equation true Use the on screen keyboard to enter the solution in the response box If there are two values enter them separated by commas y B 7 4 8 10 5 9 6 XE 2y 20

An investment earns interest compounded quarterly for 25 years How many compounding periods will there be OA 200 B 25 C 100 D 50

Find the terminal point on the unit circle determined by Use exact values not decimal approximations x y D 00 7 6 radians 0 6

Use the box method to distribute and simplify 5x 3 x 6 Drag and drop the terms to the correct locations of the table 5 3 6

Jan 15 9 05 14 AM Watch help video Subtract 5x 9x 10 from 6x 6x

Matthew rakes leaves to earn money The points in this graph represent the total amount of money Matthew earns based on the number of hours he rakes leaves Matthew wants to purchase sneakers that costs 48 How many hours does Matthew need to rake leaves to earn enough money to buy the sneakers O 5 hours O 6 hours O 7 hours O 8 hours Amount of money 40 32 24 16 8 0 Matthew s Earnings 1 2 3 Time h 4 fo 5

Which of the following functions can be used to generate the terms in the sequence 3 5 7 9 a f n 3n 1 b f n 2n 1 O c f n n 2 d f n 3n

What is the value of s for a geometric series where f 1 4 and r a 7 9375 b 8 0625 Oc 7 9375 d 0 992 187 5

For the arithmetic series 30 27 24 9 the values of a d and n are a a 30 d 3 n 8 b a 30 d 3 n 14 O c a 30 d 3 n 14 d a 3 d 30 n 8

The common difference in the arithmetic sequence O a Ob 1 0 334 c 1 1 12 2 3 d 1 2 11 7 17 5 3 12 6 12 3

The first three terms of the sequence defined by t 1 3 1 4 are O a 1 7 17 Ob 0 4 8 Oc 1 1 1 d 1 17 55

An alphabetized list of publication information about the sources used in an APA formatted essay or research paper is called a final draft O an attributions page O an in text citation a reference list

Sketch 0 45 in standard position Drag to show the angle s

Consider the parabola p x 8 3x 6 5x 8 1 For which interval A B is SP a 8 3 6 5 O b 0 3916 0 3916 O c 1 0627 1 0627 O d 7 5627 5 4373 O e 0 67109 1 45422 Clear my choice p x dx as large as possible A note about the choices for some incomprehensible reason eClass sometimes switches the position of A and B Read each option very carefully as your interval might be a backwards version of what eClass is showing as an option

Let A be the area under y e and above the x axis on 0 a Let B be the area under y e and above the x axis on 0 b B is 12 4 times A What is b in terms of a O a b In 12 4 11 40 O b b In 12 4e a 11 4000 O c b In 12 4e a 12 4 O d a In 12 4e b 1 O e b In e a 10 40

Karen has a deck of 10 cards numbered 1 through 10 She is playing a game of chance This game is this Karen chooses one card from the deck at random She wins an amount of money equal to the va the card if an even numbered card is drawn She loses 5 50 if an odd numbered card is drawn a Find the expected value of playing the game dollars b What can Karen expect in the long run after playing the game many times She replaces the card in the deck each time Karen can expect to gain money She can expect to win dollars per draw Karen can expect to lose money She can expect to lose dollars per draw Karen can expect to break even neither gain nor lose money

MotoWin Auto Superstore is thinking about offering a two year limited warranty for 983 on all new cars of a certain model The terms of the war that MotoWin would replace the car free of charge under certain specified conditions Replacing the car in this way would cost MotoWin 13 400 Suppose that under the warranty there is a 7 chance that MotoWin would have to replace the car one time and a 93 chance they wouldn t have to replace the car If MotoWin knows that it will sell many of these warranties should it expect to make or lose money from offering them How much To answer take into account the price of the warranty and the expected value of the cost from replacing the car MotoWin can expect to make money from offering these warranties In the long run they should expect to make O MotoWin can expect to lose money from offering these warranties In the long run they should expect to lose dollars on each warranty sold MotoWin should expect to neither make nor lose money from offering these warranties dollars on each warranty sold E

The Brady Matthew Camera Company has just come out with their newest professional quality digital camera the ToughPix1 The company is selling this camera only through its new mobile app at a profit of 186 per camera This purchase comes with a guarantee that barring gross negligence if the camera breaks in the first two years after purchase Brady Matthew will replace it free of charge Replacing a camera in this way costs the company 3100 Suppose for each ToughPix1 there is a 4 chance that it will need to be replaced exactly once a 1 chance that it will need to be replaced exactly twice and a 95 chance that it will not need to be replaced If Brady Matthew knows that it will sell many of these cameras should it expect to make or lose money from selling them How much To answer take into account the profit earned on each camera and the expected value of the cost of replacements of the camera Brady Matthew can expect to make money from selling these cameras hey should expect to make dollars on each camera sold In the long run Brady Matthew can expect to lose money from selling these cameras In the long run they should expect to lose dollars on each camera sold Brady Matthew should expect to neither make nor lose money from selling these cameras

Greg is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6 The number cube is fair so a side is rolled at random This game is this Greg rolls the number cube once He wins 1 if a 1 is rolled 2 if a 2 is rolled and 3 if a 3 is rolled He loses 2 50 if a 4 5 or 6 is roll a Find the expected value of playing the game dollars b What can Greg expect in the long run after playing the game many times Greg can expect to gain money He can expect to win Greg can expect to lose He can expect to lose dollars per roll money dollars per roll Greg can expect to break even neither gain nor lose money X

In Bill the Boring s dryer there are 4 black shirts 9 black sweaters and 10 gray sweaters But there are no gray shirts Bill is going to take one of these pieces of clothing out of the dryer at random to check if his clothes are completely dry What is the probability that the piece of clothing Bill takes out is gray or is a shirt Do not round intermediate computations and round your answer to the nearest hundredth X

Deandre has a bag with 8 balls numbered 1 through 8 He is playing a game of chance This game is this Deandre chooses one ball from the bag at random He wins 1 if the number 1 is selected 2 if the number 2 is selected 3 if the number 3 is selected 4 if the number 4 is selected and 5 if the number 5 is selected He loses 3 40 if 6 7 or 8 is selected a Find the expected value of playing the game dollars b What can Deandre expect in the long run after playing the game many times He replaces the ball in the bag each time Deandre can expect to gain money He can expect to win Deandre can expect to He can expect to lose dollars per selection lose money dollars per selection Deandre can expect to break even neither gain nor lose money X

Jessica won a charity raffle Her prize will be randomly selected from the 9 prizes shown below The prizes include 7 rings 1 camera and 1 headset Prizes 8888 888 a Find the odds in favor of Jessica winning a headset 0 b Find the odds against Jessica winning a headset 1 00 X 0 0 to S

Alonzo is at the grand opening celebration of a supermarket He spins a wheel with 10 equal sized slices as shown below The wheel has 2 black slices 4 grey slices and 4 white slices When the wheel is spun the arrow stops on a slice at random If the arrow stops on the border of two slices the wheel is spun again a If the arrow stops on a grey slice then Alonzo wins a gift card Find the odds against Alonzo winning a gift card 0 b If the arrow stops on a grey slice then Alonzo wins a gift card Find the odds in favor of Alonzo winning a gift card 0 00 X 0 0 S to

Bob is playing a carnival game He is blindfolded while he throws a dart at a board of 12 balloons as shown below Each balloon is labeled S for small M for medium L for large or XL for extra large The board has 1 small balloon 2 medium balloons 2 large balloons and 7 extra large balloons He hits one of the balloons at random and wins a stuffed animal of that size XL M XL XL XL S M XL L XL XL a Find the odds against Bob winning an extra large stuffed animal 0 b Find the odds in favor of Bob winning an extra large stuffed animal 0 8 0 0 X to

On 7 t red If f 1 10 7 f x is continuous and f f x dx 7 3 what is the value of f 4

on 6 t ed d out of question Suppose that a 2 6 and b 9 7 Then what is 100 O a 31 0000 O b 28 00 and Health S 7 M N O P Q R S Mathematics II for the Biological and Health Sciences Tutorial Assignments and Test Page Winter 2023 Online Assignments OC 44 60 O d 1 Oe 8 1000 100 i 1 3a 4b

The figure to the right shows the graphs of y a for a 1 5 2 4 3 7 0 42 0 67 and 0 34 They are identified by letter but not necessarily in the same order as the values just given Use your knowledge of how the exponential function behaves for various powers of a to match each lettered graph with the correct value of a Drag each value given to the right into the appropriate area below depending on which value corresponds to graph label given A B C D E 1 5 0 34 0 67 3 7 2 4 0 42 W A 15 Ay F

The cost to produce x units of wire is C 505x 2100 while the revenue is R 85x Find all intervals where the product will at least break even BETER Select the correct choice below and if necessary fill in the answer box to complete your choice OA The interval is Type your answer in interval notation Use integers or fractions for any numbers in the expression OB The product will never break even

raph the rational function x 1 x 4 x 3 A OB GEXE O C Ay G O D Ay

Find the value s of the function on the given feasible region Find the maximum and minimum of z 7x 24y 0 6 1 2 5 5 0 C OA 35 0 OB 144 0 OC 35 144 OD 111 25 144

1 Select one More on Polynomials Question 3 Which information is true about f x pictured to the right 01 O f x is even O f x is odd f x is both even AND odd Of x is neither even norodd ANA 311 2 04 2

A county is planning to expand its train service In studying the current service the county planner looked at which train stations are along or not along vari train lines The Venn diagram shows this information for three of the lines All county train stations Blue Line stations Nara Lahti Warren Erie Quilmes Metz Green Line stations Okene Orange Line stations Zama York Volos Fes Athens Ilion Graz Ponce a Select all the train lines that do not have a stop at Lahti Orange Line Green Line Blue Line Orange Line b How many stations are only along the Green Line 0 c Which stations are along neither the Blue Line nor the Orange Line nor the Green Line Choose all that apply Erie Fes Athens Lahti Quilmes Metz Nara Volos Warren Graz Okene York X Ilion Ponce Zama