Functions Questions and Answers

3 Subtract 5 31 O A 313 O B 21 O C 13 O D 23

m t Let This Happen To You Use the data for the country of New Finlandia in the following table to calculate the following REAL GDP PER CAPITA 2005 PRICES YEAR 2010 2011 2012 2013 2014 41 761 42 896 42 359 43 462 43 203 ber from the previous chapter that the average annual growth rate for relatively short periods can be approximated by averaging the growth rates of age increase in real GDP per capita between 2010 and 2014 is 3 45 Enter your response rounded to two decimal places annual growth rate in real GDP per capita between 2010 and 2014 is Enter your response rounded to two decimal places

Absolute value function Cube function Square function Reciprocal function Identity function Square root function Cube root function Constant function Drag the function to the appropriate area below

Find the value of the question mark 30 18 2

oblem 1 The graph of a function is given Use it to answer the following questions Do that for each graph graph continues and does not stop a Open interval s where the function is increasing if anywhere b Open interval s where the function is decreasing if anywhere c Open interval s where the graph is concave up if anywhere d Open interval s where the graph is concave down if anywhere e Where the graph has a point of inflection if any f Where the function reaches a local maximum if any g Where the function reaches a local minimum if any h Where the function reaches an absolute maximum if any i Where the function reaches an absolute minimum if any j Describe the end behavior of the function 1 6 5 2 1 0 0

Problem 3 The portion E of Earths surface visible from a spacecraft depends on the height z above the surface of Earth The relationship is I E x 2R 2x where R is the radius of Earth a Evaluate the limit of E x as o numerically algebraically and graphically b Explain the meaning of the limit in part a in terms of the visible portion of Earths surface

First Oak Eagle View River Point West United 2 Compounded Annually 5 Compounded Annually Ava opened an account 1 First Oak with 5000 Zoe started an account with 4000 at West United No additional money was deposited or withdrawn from the accounts 6 Simple 8 5 Simple How much more money will be in Ava s account than Zoe s at the 1 2 3

ED THIS Read Section 1 7 Pages 20 26 Watch KCVS 1 6 1 7 IWES 1 5 1 6 Perform the following calculations to the correct number of significant figures View Available Hint s VAEO

8 What transformations of parent function f x 2 2 x result in g x x 48 4

6 Write the first four terms of the sequence defined by an 2 if n 1 a1 7 if n 1

Line jin the xy plane contains the point 2 8 and is parallel to the line with equa 7 What is the slope of line j y x 3 3

7 x 2x 4x 5 x 2 9 3x4 6x 27x 33x 61 3x 9 4 8 x 7x 5x 45 x 7 10 6v 56v 106v 57 6 8

U The set of ordered pairs t d where t is the time in seconds after someone jumps out of a plane at 4000 meters to go skydiving and d is the displacement above the ground

Jeff has a lawn mowing business and needs an average of 25 minutes to cut the grass on lawns between 900 and 1200 square feet He has already mowed one lawn of this size today and is planning on mowing more lawns of this size between 9 am and 1 pm a Given his time constraints use set notation to describe all the possible number of complete lawns L that Jeff can have mowed by the end of the day b Use interval notation to describe the range of lawn areas that Jeff can mow on this day given his time constraints

Click the following link to view GDP data from FRED Then use that data to answer the following questions For this exercise you will need to enter data from FRED for nominal gross domestic product GDP and real gross domestic product GDPC1 Using the data from FRED enter the values for the second quarter of 2023 shown as 2023 04 01 in Fred for the following series IDS Enter your responses exactly as they appear in FRED Series ID Value GDP GDPC1 26834 953 bil 20404 088 bil of chained Given these values the GDP deflator for this period is Enter your response rounded to two decimal places GDP 26 643 24 901 23 159 21 417 19 675 17 933 16 191 14 449 12 707 10 965 9 223 U S Nominal and Real GDP Q2 11 Q2 15 02 19 02 Real time data provided by Federal Reserve Economic Dat Federal Doconio Bank of Saint Louis

Reproduce the given computer generated direction field Then sketch an approximate solution curve that passes through each of the indicated points sin x cos y dx d Y 0 2 52 2 0 N 2 y 0 4 2 PUSSIONS Used X 2 y y

nts Book t A builder has located a piece of property that she would like to buy and eventually build on The land is currently zoned for four homes per acre but she is planning to request new zoning What she builds depends on approval of zoning requests and your analysis of this problem to advise her With her input and your help the decision process has been reduced to the following costs alternatives and probabilities Cost of land 2 million Probability of rezoning 0 60 If the land is rezoned there will be additional costs for new roads lighting and so on of 1 million If the land is rezoned the contractor must decide whether to build a shopping center or 1 450 apartments that the tentative plan shows would be possible If she builds a shopping center there is a 60 percent chance that she can sell the shopping center to a large department store chain for 5 million over her construction cost which excludes the land and there is a 40 percent chance that she can sell it to an insurance company for 4 million over her construction cost also excluding the land If instead of the shopping center she decides to build the 1 450 apartments she places probabilities on the profits as follows There is a 60 percent chance that she can sell the apartments to a real estate investment corporation for 2 000 each over her construction cost there is a 40 percent chance that she can get only 2 400 each over her construction cost Both exclude the land cost If the land is not rezoned she will comply with the existing zoning restrictions and simply build 400 homes on which she expects to make 3 500 over the construction cost on each one excluding the cost of land a What is the expected value for the rezoned shopping center if the rezoning cost is included but land cost is excluded Do not round your intermediate calculations Enter your answers in millions rounded to 2 decimal places Negative amounts should be indicated by a minus sign Expected value pected value wwwwwwww million What is the expected value for the rezoned apartments if the rezoning cost is included but land cost is excluded Do not round our intermediate calculations Enter your answers in millions rounded to 2 decimal places Negative amounts should be indicated wa minus sign million

15 Nuclear explosions require a specific amount of mass to trigger and self sustain a nuclear chain reaction That mass is called the OA neutron mass OB critical mass O C mass defect D neutrino

4 Adenosine triphosphate is the energy source for work in the cell It provides energy to the cell and OA activates compounds for some reactions by transferring a phosphate group OB activates enzymes by transferring phosphate groups to change the shape of the enzyme O C deactivates compounds for some reactions by transferring a phosphate group OD transfers its adenosine group to DNA

1 Latex DNA and cellulose are all examples of O A natural monomers OB natural polymers OC monomers OD synthetic polymers

3 owing ro given fur a State the domain of the function b Find f x h and fully simplify your result fully expand the expression c Find the difference quotient of f and fully simplify your result meaning simplify and eliminate h I a f x 3x 2 b f x r 4 1 2x 1 J x c f x

Problem 4 Epidemiologists in a particular town estimate that t days after the flu begins to spread in the town the percent of the population infected by the flu is approximated by p t t t for 0 t 5 a Evaluate p 1 and interpret what it means Also be sure to include the units b Find the difference quotient p t h p t h and fully simplify your answer

14 A simplified version of photosynthesis can be represented as carbon dioxide combining with water to form glucose and oxygen 6CO 6H O C H 0 60 In this reaction is oxidized O A carbon dioxide O B hydrogen C carbon O D oxygen

7 During the electrolysis of an aqueous solution of sodium nitrate a gas forms at the anode what gas is it OA Hydrogen OB Sodium O C Oxygen OD Water

Question 6 of 13 Calculate the average rate of change of the function f x 6mx b where m and b are constants on the interval a a h assuming h 0 Simplify your answer as much as possible Express numbers in exact form Use symbolic notation and fractions where needed Simplify your answer completely average rate of change

K Some questions make use of the Interactive Graphing Tool in order to draw a parabola using two points Click the icon to view instructions for the Interactive Graphing Tool Draw a solid vertical parabola overlaying the dashed parabola on the graph Use the vertical parabola tool button on the graphing palette to draw a solid vertical parabola Place the first point at the vertex of the parabola shown as the solid dot on the graph and place the second point at another location on the parabola shown as the dashed curve on the graph Click to enlarge graph Careful Be sure to use a second point that is exactly on the parabola causing the dashed curve to be completely covered D Ay 10 8 8

19 A chemical reaction has the equation 4AI s 3 O g 2Al O s What type of reaction is this O A Double displacement O B Synthesis OC Single displacement D Decomposition

16 Two atoms bonded together will remain some distance apart minimizing the O A potential energy of the bond OB number of valence electrons in the bond OC bond distance O D partial charge of the bond

11 The appropriate substitution to solve 9 3x dx is x A 3 tane B 3 seco C 3 tane D 3sing 12 If the integral finx dx a 1 then the value of a is A B e Ce D

What is the correct x component of the resultant of all the external forces applied to the component shown below F 750 N 45 F 625 N OF2 cos30 30 O F2 sin 30 F 850 N

6 Which of the following are the factors of t4 81 O A t 3 t 3 OB t 3 2 t 3 OC t 9 t 9 D t3 t 3 t 9

9 What is the value of j in the equation 14 3 10 OA 16 OB 4 OC 2 OD 2

17 What is the slope of a line that passes through 14 13 and 7 0 A B C D 21 13 21 13 13 21 13 21

8 What quadrant would the ordered pair 4 6 fall in OA III OB I OC IV OD II

5 Using the point slope formula what is the equation of the line that passes through the points 1 5 and 0 0 O A y 5x OB y 5x 10 O C y 5x 1 D y x C

4 What is the equation of the line that passes through the points 2 2 and 0 5 O A y x 5 OB y x 5 O C y 3 2x 5 O D y 3 2x 5

To determine the mean number of children per household in a community Tabitha surveyed 20 families at a playground For the 20 families surveyed the mean number of children per household was 2 4 Which of the following statements must be true A The mean number of children per household in the community is 2 4 B A determination about the mean number of children per household in the community should not be made because the sample size is too small C The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community D The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community

K Suppose your weekly allowance from your parents is 50 and your part time job pays 10 per hour The slope of the line plotting the relationship between the hours worked per week the horizontal axis and the income per week the vertical axis is Enter your response as an integer Suppose you start with 10 hours of part time work and then decide to increase your time working by 3 hour s By how much will your weekly income increase 79 Enter your response as an integer Suppose you start with 10 hours of work and then decide you need additional income of 40 per week How many additional hours would you have to work hours Enter your response as an integer

6 12 points Suppose z x y e and x y are each functions of variables u v Given that r dx y du v v 1 u find and in terms of x y u v du 0 y du 0 u sin v

Read paragraph 5 But talk can have great value you have to think of it as a bridge You have to think of the General Assembly as a place where bridges are built between peoples How does the metaphor develop Roosevelt s ideas in the speech O by highlighting the difference between words and action O by creating an image of making connections O by illustrating the divide between countries O by emphasizing that meaningful changes take a long time

Function Domain Range w s Name Nabaa AL Sommarhale State the Domain Range of each relation then state whether each graph represents a function 1 7 10 13 2 DISEN 5 8 11 7 14 f 3 6 9 12 15 An

How many different sections and in what ranges of x would be needed to obtain functions for internal loads in the structure shown in the figure OA It needs 4 sections 0 to 2 2 to 5 5 to 8 and 8 to 10 OB It needs 5 sections 0 to 2 2 to 4 4 to 6 6 to 8 and 8 to 10 OC It needs 6 sections 0 to 2 2 to 4 4 to 5 5 to 6 6 to 8 and 8 to 10 Internal loads as functions of position Let s do a quick check how many different sections a what ranges of x would be needed to obtain functions internal loads in the structure shown below Please p your answer in PlayPosit A 2m IKN ZkN m 2m RISKU zm 3KN A It needs 4 sections 0 to 2 2 to 5 5 to 8 and 8 to 10 B It needs 5 sections 0 to 2 2 to 4 4 to 6 6 to 8 and 8 to 10 C it it needs 6 sections 0 to 3 20 nause it

23 f x 22 x 4 3 24 3 2 x x x 6 Domain Range x 1 3 if x l Topic 3 Piecewise Functions Identify the domain and range of each graph below State the location and type of any discontinuties Domain Discontinuities Domain if x 4 if 4 x 1 x int Extrema Graph the function below Identify the domain and range then state the location and type of any discontinuties Increasing Interval Decreasing Interval End Behavior 2x 1 Domain 28 f x Range Topic 4 Average Rate of Change Find the average rate of change of the function on the given interval 27 f x 2x 3x 1 3 2 Range y int x 3 Range Discontinuities Discontinuities 10 5

B Write It is the weekend Tell about your family s chores Look at 1B for help It is the weekend We are doing chores 1 I am 2 3 4 5 is is is and are

By hand convert the decimal number 21 625 to a a binary number b a binary floating point number in engineering notation keep the exponent as a decimal numbe Problem 2 required submission Handwritten or printed all steps to obtain the answers incl the final answers

By hand convert the binary number 1001 010 into a decimal number Problem 1 required submission Handwritten or printed all steps to obtain the answers incl the final answers

Question 5 of 13 Calculate the average rate of change of the function f x 5x on the interval a a h assuming h 0 Simplify your answer completely Give your answer as a whole number average rate of change

5 a b c Calculate the average rate of change of f x on the interval a a h assuming h 0 Simplify as much as possible Then compute for a 7 and h 2 1 f x 2 5x f x x f x x 1 a 1 Conc 2031 Time hours

1 1 9 ale given x 2x 3 For questions 3 and 4 evaluate given g x 3x x 3g 2x 1 For questions 5 and 6 evaluate given h x 5 h 7 11 Square Root 71 x 1 12 Cube Root A g 3x Topic 2 Parent Functions Transformations and Graphing For each function family below give the parent function and sketch the shape of its graph 7 Linear 8 Absolute Value 9 Quadratic 10 Cubic 4x 7 if x 3 r 2x if x 3 6 h 3 13 Reciprocal 14 Greatest Integer

For the position function s t 16t 108t complete the following table with the appropriate average velocities The make a conjecture about the value of the instantaneous velocity at t 1 1 1 5 Time Interval Average Velocity 1 2 Complete the following table Time Interval 1 2 1 1 5 Average 0 Velocity Type exact answers Type integers or decimals 1 1 1 1 1 1 1 1 01 1 1 01 1 1 001 1 1 001 7