Functions Questions and Answers

x y 16x 14y 32 0 is the equation of a circle with center h k and radius r for h and k and T

The plot below represents the function f x 5 4 3 2 8 x 6 4 2 NO Evaluate f 3 f 3 Solve f x 3 1 2 3 O

se Maclaurin series to evaluate this limit r ln 1 14x arctan r lim I 0 I

1 point In the figure below a rectangular piece of sheet metal was cut diagonally through its center making a triangular shape A right angle is shown on figure What is the length of the diagonal cut c if edge a is 22 inches long and edge b is 25 inches long 33 3 inches 31 8 inches 36 2 inches C

Vrite an equation of the line below 6 5 8 6 5 4 3 4 5 6 9 8 1 0 0 0 X 00

A TV studio has brought in 6 boy kittens and 9 girl kittens for a cat food commercial The director is going to choose 7 of these kittens at random to be in the commercial What is the probability that the director chooses 4 boy kittens and 3 girl kittens Round your answer to three decimal places X

40Listen In f x sin kx the period will be greater than 27 if Oa 2 k 1 Ob 0 k 2 Oc 0 k 1 d 1 k 2

Their responses are given below 13 18 7 Number of miles 12 9 8 2 2 15 17 19 2 12 a Complete the grouped frequency distribution for the data Note that the class width is 5 Number of miles 1 to 5 10 3 6 to 10 11 to 15 16 to 20 Frequency 1 0 0 0 hey biked last week b Construct a histogram for the data Frequency 5 4 1 to 5 11 to 15 6 to 10 Number of miles 16 to 20

A certain college graduate borrows 8661 dollars to buy a car The lender charges interest at an annual rate of 12 Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate dollars per year determine the payment rate that is required to pay off the loan in 6 years Also determine how much interest is paid during the 6 year period Round your answers to two decimal places Payment rate I Interest paid dollars per year dollars

What is the tangent line to when x 2 4 O a y 0 9281x 108 1897 O b y 3 1554x 100 6168 O c y 3 1554x 7 5729 O d y 317 4844x 661 3458 O e y 3 1554x 108 1897 O f This tangent line does not exist y x 4 x

99 Determine whether the vector field F x y Y 1 x is conservative or not If it is find a potential function and use it to evaluate the line integral 1 F dr t 2t cos t 1 t 3 where C is the curve defined by r t e sin y i tan x e cos y j

A coin is flipped and a number cube is rolled The tree diagram below shows the possible outcomes Use t diagram to answer the questions Coin heads tails Number cube 2 3 5 6 2 3 4 5 6 a How many outcomes are there outcome s Outcome heads 1 heads 2 heads 3 heads 4 heads 5 heads 6 tails 1 tails 2 tails 3 tails 4 tails 5 tails 6 b How many outcomes involve heads and an even number outcome s c How many outcomes do not involve rolling 5 outcome s X

28 784 4 5 45 900 24 The perimeter of a rectangle is 40 inches and the area of the rectangle is 96 square inches Use a system of equations to find the dimensions of the rectangle 96 4 384

Use the given information to find the linearization of h x at x 4 Then use your linearization to approximate h 3 9 h 3 13 1 h 3 18 2 h 4 8 9 h 4 31 0 Write your exact numerical answer in the box below

Without using a calculator find the exact value of sin 1 Giv Give your angle in radians use pi for

The relative rate of change of a differentiable function s given by y f x 100 f x f x What is the relative rate of change of a population in x 20 months of a Gompertz growth function given P x 224e O a 1 31107 O b 0 00140 O C 0 02688 O d 0 00001 O e 1 87920 f000390 0 0522e 0 36

19 Five hundred dollars was invested in an account earning continuously compounded interest If the investment grew to 1245 after 10 years what was the annual interest rate Find an expression for the exact interest rate and simplify as much as you can without using a calculator 20 One thousand dollars is deposited into an account earning continuously compounded interest If

Independent events A spinner is used for which it is equally probable that the pointer will land on any one of six regions Three of the regions are colored red two are colored green and one is colored yellow If the pointer is spun three times find the probability it will land on green every time OA 2 27 OB 9 O C 1 18 OD 1 27

My character in the classic Xbox game Knights of the Old Republic wants to create a new lightsaber I have decided that the following attributes and what percent of my decision they represent will determine which crystal I choose Cost 15 Attack Modifier 32 Damage 34 Regeneration Force Points 19 The following table lists the crystals I will consider and their ratings out of 10 Which crystal is the best fit for my character s lightsaber Crystal Rubat Damind Eralam Sapith Cost Attack Modifier 1 2 3 4 1 4 5 5 Damage 1 1 5 7 Regeneration Force Points 3 2 0 0

A swimming pool has a length of 30 ft and a width of 15 ft What is the perimeter of the swimming pool 15 ft 30 ft P ft

Which function has a greater value when x 47 Function A Function B Miles 1 2 3 Hours 47 94 141

6 points 12 The marginal cost C in dollars of manufacturing x cell phones in thousands is given by C x 5x 200x 4000 a How many thousands of cell phones should be manufactured to minimize the margina What is the minimum marginal cost

Given rhombus ABCD find the perimeter if AE 9 and BE 12 B E C

3 Function notation and meaning If you are given a context and a function in a table graph or equation you can explain what f 3 means and f x 3 means You can also evaluate f 3 and solve for x when f x 3 Example If the number of forks y used at a restaurant is a function of the number of customers x we can use the notation y f x What would be the meaning of each of these equations or expressions in words A f 23 37 B f x x C f 151 9 D f x 2x 9

1 Use transformations of the graph of the parent function f x 1 to graph g x 1 X X 3 2

Express the set in roster form B x XEN and x 2 Choose the correct answer below OA B 2 3 4 5 OB B 2 3 4 5 OC B 2 OD B 3 4 5 6 OE B 2 3 4 5 100 OF B 3 4 5 6 OG B

Use KKT to solve the following problem min x 2y subject to 5x y 3 2x y 26 Find the value of the variables and the Lagrange multiplier Express your answers in fraction form X II 11 A 2 11 11

8 6 points Analyze and sketch a graph of the function Label any intercepts relati extrema points of inflection and asymptotes f x 2x 9 x2

1 Create your own parabola Sketch a graph AND determine an equation that satisfies the given y intercept at 7 the vertex in quadrant 3 see diagram of quadrants no x intercepts vertical stretch Quadrant Quadrant 2 1 Quadrant Quadrant 3 4

Apples sis and concepts with mited knowledge and Level 1 2 2 2 5 2 8 Applies skills and concepts with some knowledge and understanding with errors Communication Rubric Level 2 3 0 3 2 3 4 No justification is provided to support the final answer and lacks mathematical terminology Applies skills and concepts with considerable knowledge and understanding with minor errors Presents a justification of answers but it is incomplete and uses some mathematical terms Level 3 3 5 3 7 4 0 Usually presents a clear justification of answers using appropriate mathematical terminology with few errors All questions must be completed using concepts discussed in class and show all work for full marks Applies skills and concepts with no errors or insignificant errors Level 4 4 2 4 6 5 0 Always presents thorough and clear justification of answers using appropriate mathematical terminology APPLICATION Choose ONE of the following word problems to answer below 1 Garth Motors has been selling an average of 50 new cars per month at 800 over the factory price They are considering an increase in this mark up A marketing survey indicates that for every 20 increase they will sell one less car each month What should their new mark up be to maximize income 2 Find two numbers whose difference is 64 and whose product is a minimum

A 3 month 16 000 treasury bill with a simple annual discount rate of 0 22 was sold in 2016 Assume 365 days in year a Find the price of the treasury bill T bill b Find the actual interest rate paid by the Treasury a The price of the T bill was 8 8 Round to the nearest cent as needed

Assume the hold time of callers to a cable company is normally distributed with a mean of 5 7 minutes and a standard deviation of 0 5 minute Determine the percent of callers who are on hold between 5 6 minutes and 6 4 minutes Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table Round to two decimal places as needed

Find an equation for the line below By 51 4

Graph the solution to the following system of inequalities 5x 4y 16 x 0 y20 10 B 30 10 X

Ann will donate up to 480 to charity The money will be divided between two charities the City Youth Fund and the Educational Growth Foundation Ann wou like the amount donated to the Educational Growth Foundation to be at least three times the amount donated to the City Youth Fund Let x denote the amount of money in dollars donated to the City Youth Fund Let y denote the amount of money in dollars donated to the Educational Growth Foundation Shade the region corresponding to all values of x and y that satisfy these requirements 445 360 329 240 200 110 120 80 40 120 140 200 240 260 320 360 430 440 42 120 5

5 The population of 4 different species of fish living in a small local lake are given to the functions below The population of each in thousands is a function of time ir years Write a sentence that describes each population a a t 3 5t 20 b b t 10 1 057 c c t 15 5e 0 01 d d t 4cos 2mt 5

Which of the following is a pure imaginary number Enter a b c d or e a 36 b 36 c 1 d 52 e 4 3i

f x sinxx i 8 points Find the intervals where f is increasing or decreasing ii 8 points Show that cosr 1 x3 6 2 24 for every real number x A solution with a graph and without any mathematical arguments will not get any credits

Assuming that the annual rate of inflation averages 3 over the next 15 years the approximate costs C of goods or services during any year in that decade will be modeled by C t P 1 03 where t is the time in years and P is the present cost The price of an oil change for your car is presently 28 89 Estimate the price 15 years from now Round your answer to the nearest cent

tions below To ride a roller coaster a visitor must not be less than 52 inches tall Use h to represent the height in inches of a visitor able to ride 0 At the airport each piece of luggage to be checked in must weigh less than 60 pounds Use w to represent the weight in pounds of a piece of luggage that can be checked in D 020

On the day of a child s birth a parent deposits 35 000 in a trust fund that pays 4 interest compounded continuously Determine the balance in this account on the child s 28th birthday Round your answer to two decimal places

Match the exponential function with its graph f x 2 x O 4 y 10 8 6 4 2 Need Help 1 2 2 2 Read It y 10 8 6 4 2 4 0 1 6 2 8 4 10 X X Y 2 2 20 0 1 15 10 5 10 8 4 y 6 2 10 2 2 2 4 X X

5 points Find 2 f 3 f 4 if f is defined recursively by f 0 1 f 1 1 2 3 we have f n 1 f n 2 1 2 and for

4 Let K be a field and a K Prove that K x x a K

0 2 Represent the function f x x0 as a power series Find the following coefficients co 1 5 C C1 C2 C3 cn x 4 n n 0

Josh has 12 coins in his pocket He has four times as many dimes as quarters The total value of his money is 1 00 How many quarters dimes and nickels does he have Enter a b c d or e a 2 quarters 2 dimes 8 nickels b 2 quarters 4 dimes 6 nickels c 1 quarter 4 dimes 8 nickels d 2 quarters 8 dimes 2 nickels e 1 quarter 4 dimes 7 nickels

ve the following linear recurrence for the kth term In particular determine the value 40 ak 2 0 6ak 1 1ak 1 where do 1 9 and a 0

How fast in miles per hour must a car travel to go 800 miles in 16 hours mph

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x, y) point. y = -2x² - 28x - 108

Write the compound statement in symbolic form. Let letters assigned to the simple statements represent English sentences that are not negated. If commas do not appear in compound English statements, use the dominance of connectives to show grouping symbols (parentheses) in symbolic statements. We have power if and only if it's not true that both the lines go down and the transformer blows. Let p represent the simple sentence "The lines go down," q represent the simple sentence "The transformer blows," and r represent the simple sentence "We have power." The compound statement written in symbolic form is