Functions Questions and Answers

1 Answer the following questions using the graph of the function f x below 6 pts M ESUS In sibeqal sims 10touren a lim g x b lim g x 17 C lim g x 2 MAXI d lim g x morsinoleu TOY TO1 qooxe bewolls abie e The equations of the vertical asymptotes nofoviups to 2AD stigan 7 3 6 TOT 08 11 TOSIDING THOSE OF O 996 w woy guido do bus amaldorq gaivloe ai voy bis 01 a G

17 65 Determine the vertical and horizontal components of reaction at the pin support A and the angular acceleration of the 12 kg rod at the instant shown when the rod has an angular velocity of 5 rad s A 0 6 m

a A Particle is released during an experiment It s Speed minutes after release is given by uv t 0 5t lot where u t is in meters per second How far dues the Particle travel during the first 5 seconds

Good Times Bakers works out a demand function for its cookies and finds it to be g D X 967 25x where g is the quanity of cookies sold when the price per Cookie is x cents Find the elasticity function Find the elasticity at a price of 0 10 Per Cookie X 10 and state whether the demand is elastic or inelastic at that price At this price will raising the price increase revenue Find the price where the Revenue is a maximum

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit given the following revenue R X and cost C x functions R X 5X and CC X 0 001x2 1 2x 60

11 Given f x 4 x 2 x 5 3 x 2 x 6 determine a 3 pts the x intercept s if any give x coordinate s b 3 pts vertical asymptotes in equation form c 3 pts horizontal asymptotes in equation form d 3 pts domain interval notation

6 Given y 9 sin 8x 7 6 determine a 4 pts the amplitude b 4 pts the period 4 pts the phase shift and direction

7 Solve the following equations State exact answers a 5 pts log x log x 2 3 b 5 pts 4x 23x 5

3 8 5 pts Find the inverse of f x x 5 Don t forget to show your w

5 Consider the following triangle a B b If A 55 and b 19 find the values of a 3 pts B b 3 pts a c 3 pts c

z x e In x 2 0 3

g x 22 x 1

The graph of a polynomial function is given What is the smallest degree that the polynomial could have The smallest degree the polynomial could have is Simplify your answer AY th

Graph the equation y 5 4 3 2 1 4 3 2 7 1 1 3 2 3 x 2 2 3

8 4 x intercept 16 y intercept 0 12 8 4 4 8 12 16 Use the graph to identify the x and y intercepts of the graph Note the scale on each axis since they may not be the same 4 0 8

Determine whether this table represents a probability distribution P x x 0 4 3 4 0 08 0 09 0 14 0 97 No because x has negative No because P x has negative No because P x is not 100 No because x 0 Yes because P x is 100

Fill out the black to make the given table below a probability distribution 8 0 1 2 3 4 P x 0 06 0 07 0 5 0 24

The veterinary researchers wanted to know if housing might be related to whether or not a horse develops enteroliths Attached are side by side charts of housing for horses with enteroliths cases and horses without controls Based on these charts it is reasonable to conclude that case Housing by case status control Category largepaddock pasture smallpaddock stall Ponel variable Diagnosis OA it cannot be determined from the pie chart OB cases and controls are equally likely to be housed in a pasture OC cases are less likely to be housed in pasture

The following are the heights in inches of the players in four basketball teams for a recent season Use classes of width 2 starting at 64 5 to construct a histogram Choose the correct histogram below O A Kouenbau NOTO O C Frequency 62840 64 5 66 5 68 5 70 5 72 5 74 5 76 5 78 5 80 5 Height in 64 5 66 5 68 5 70 5 72 5 74 5 76 5 78 5 80 5 Height in Q Q Team A Team B Team C Team D Q Q Data table OB Frequency CAONG O D Frequency 64 5 66 5 68 5 70 5 72 5 74 5 76 5 78 5 80 5 Height in 6284 This question 1 point s possible 64 5 66 5 68 5 70 5 72 5 74 5 76 5 78 5 80 5 Height in 73 73 66 69 73 80 71 67 72 65 66 80 74 80 70 80 68 68 79 67 74 78 68 70 72 69 73 69 76 65 77 71 68 78 69 65 75 68 69 70 70 69 68 65 75 73 76 69 77 73 70 67 68 77 71 66 78 65 75 77 68 75 68 73 D X Q Q S

Use the graph of f x to evaluate the following 6 5 4 3 2 1 f x 1 1 2 3 X 4 5 6 Average rate of change of f x over the interval 1 4

7 Determine whether n 1 n n converges or diverges with justification

The true price of a gift you purchase by mail order is 18 57 but you are billed for 19 31 Find the absolute and relative errors The absolute error is Type an ingeter or a decimal The relative error is Round to one decimal place as needed

Choose the best answer to the following question Explain your reasoning with one or more complete sentences What does a blood alcohol content BAC of 0 08 gm 100 mL mean Choose the correct answer below O A A person with 4 liters of blood has 0 08 x 40 3 2 grams of alcohol in his blood because O C O D CL A person with 4 liters of blood has OB A person with 4 liters of blood has 0 08 x 40 3 2 grams of alcohol in his blood because 0 08 represents the number of grams of alcohol in a liter of blood and that needs to be incr a factor of 40 A person with 4 liters of blood has 0 08 gx40 100 mL x 40 3 2 g 4L 0 08 0 02 grams of alcohol in his blood because dividing the grams of alcohol by the number of liters yields grams per liter 4 0 08 0 002 grams of alcohol in his blood because 4 L is 40 times as much as 100 mL 40

Question 11 Match graphs with functions f x 1 5 arctan x 3 f x 2 arctan x 2 f x 1 5 arctan x 3 f x 2 arctan x 2 a b C d 4 4 3 2 4 3 1 2 1 4 2 F 1 4 5 4 3 s 2 3 2 1 1 2 H 5 4 3 0 10 pts 3 2 3 to

0 10 pts 399 Details Evaluate the following expressions Your answer must be an exact angle in radians and in the interval 0 Example Enter pi 6 for 6 1 3 2 a cos b cos 2 2 c cos 0

0 10 pts 399 Details Evaluate the following expressions Your answer must be an angle in radians and in the interval a sin 0 b sin 2 2 c sin 1 22 2 2

The polynomial sequence defined by S k k 4k 8 satisfies the third order homogeneous linear recurrence relatic S k C S k 1 C S k 2 C3S k 3 0 for k 3 Determine the values of C C2 and C3 and C C and C3

7 Suppose there are 70 million people in the labor force out of which 60 million are employed then the unemployment rate is A 7 B 10 C 14 28

6 Question 4 y 0 10 pts 399 Details 5 4 3 2 1 8 7 6 5 14 1 1 2 5 6 7 8 1 2 3 4 5 10 6 Write an equation for the function graphed above

0 10 pts 399 Details 6 5 4 3 2 3 2 2 et S LA The graph above is a graph of what function Oy csc x Oy cot x Oy tan x Oy cos x Oy sec x

Which of the following graphs is the correct plot of y 5 4 3 2 1 T 2 3 4 5 5 4 3 2 1 1 2 3 3 4 5 4 6 5 4 3 2 1 2 3 4 a st 6 2 3 4 2 cos x 5 5 4 3 2 1 2 3 4 5 3 5 6 p

Extra Credit From a truly free market capitalist perspective how is inflation a beneficial process our myriad discussions on this concept and the supplemental readings will be very helpful here Up to 10 EXTRA CREDIT points

5 Inflation can be measured by A the percentage change in the CPI B the absolute change in the CPI C the absolute change in the GDP deflator D the percentage change in GDP

42 What is the current U S unemployment rate Why has it changed over the last 15 years or so 4 points

45 Why is consumption spending insufficient to explain economic growth and rising standards of living 5 points

27 All of the following will increase the economy s potential output EXCEPT A an increase in physical capital B a decrease in the aggregate price level C an increase in human capital D technological innovation

43 We have talked quite a bit about inflation Consider the Do rising oil prices following question and evaluate cause inflation 4 points

41 What is the philosophical economic essence of Keynesian doctrine or Keynesianism that emerged from the experience and attempted explanations of the Great Depression What would all Keynesians believe to be Keynesian 4 points

40 Why is it incorrect inappropriate to say that governments invest the national savings 4 points

Starting at age 30 you deposit 2000 a year into an IRA account for retirement Treat the yearly deposits into the account as continuous income stream If money in the account earns 6 compounded continuously how much will be in the account 35 years later when you retire at age 65 How much of the final amount is interest What is the value of the IRA when you turn 65 Round to the nearest dollar as needed

Find the consumers surplus and the producers surplus at the equlibrium level for the given price demand and price supply equations Include a graph that identifies the consumers surplus and the producers surplus Round all values to the nearest integer p D x 36 0 06x p S x 11 0 04x The value of x at equilibrium is 250 The value of p at equilibrium is 21 The consumers surplus at equilibrium is 1875 The producers surplus at equilibrium is 4

Fill out the black to make the given table below a probability distribution x 0 1 2 3 4 P x 0 04 0 16 0 43

Determine whether this table represents a probability distribution P x X 0 2 2 4 0 18 0 1 0 14 0 86 Yes because P x is 100 O No because P x is not 100 No because x has negative O No because x 0 No because P x has negative

For the proprablility distribution table below P x 0 05 0 1 2 3 X 4 0 1 2 3 4 Find the mean Round to two decimal places 0 08 x 0 2 0 09 0 58 x Find the standard deviation Round to three decimal places xP x x P x

30 A park ranger at point A observes a fire in the direction N25 26 E Another ranger at point B 4 miles due east of A sites the same fire at N58 34 W Determine the distance from point B to the fire Round answer to two decimal places 4 08 miles O 3 43 miles O 3 63 miles O 1 73 miles 2 05 miles

cautious and decide to save more of their income of saving and investment according to neoclassical economics the interest rate will decrease saving and investment will decrease the interest rate will decrease saving and Investment will increase the interest rate will increase saving and investment will decrease the interest rate will increase saving and investment will increase Question 50 2 points Saved 4 Listen Suppose there are 20 million part time workers and 100 million full time workers in an economy 3 million of the part time workers switch to full time work with no change in the labor force participation rate As a result the official unemployment rate will fall the size of the labor force will increase official unemployment rate will rise official unemployment rate will remain unchanged

ics does NOT argue the market system has the self adjusting mechanism that fixes unemployment and recession in the long run as long as wages prices and interest rates are flexible government regulation is generally good for the overall economy GDP is determined by supply factors such as resources and technology not aggregate demand raising minimum wage generally creates unemployment

Real GDP has gone up although the living standard enjoyed by the average citizen Real GDP per capital has gone down Why there was greater nominal GDP growth there was greater population growth there was greater inflation there was greater investment

The rate at which people are becoming infected in person per day during the outbreak of a disease was approximated by the function mentioned below where x is in days and x 0 corresponds to the start of the outbreak Complete parts a and b below f x 6xe X a Find the function F x that gives total number of people who have become infected by day x given that 12 people choice were infected when x 0 Select the correct choice below and fill in the answer box to complete your O A To find F x evaluate the antiderivative of f x Therefore F x Type an exact answer B To find F x evaluate the derivative of f x Therefore F x Type an exact answer b Find the total number of people who have become infected by the end of 2 weeks The total number of people who have become infected with the disease by the end of 2 weeks is Round to the nearest whole number as needed Do not round until final answer

7 Write the equation for the following function in vertex form 9 2 8 8 2 3 2 0 5 0 1 2 3 Aos x 2 11 65 y a x 1 b 0