Functions Questions and Answers

An inferior product with a large advertising budget sells well when it is introduced but sales fall as people discontinue use of the product Suppose that the weekly sales S are give 600t 0 t 2 2 where S is in millions of dollars and t is in weeks After how many weeks will sales be maximized weeks S

A manufacturer estimates that its product can be produced at a total cost of C x 55 000 100x x3 dollars If the manufacturer s total revenue from the sale of x units is R x 4000x doll determine the level of production x that will maximize the profit Round your answer to the nearest whole number units Find the maximum profit Round your answer to the nearest dollar

1 Given f x 2x and g x x 4 determine the expression for f g x

Ryan Plastics has a target debt to equity ratio of 0 25 Its cost of equity is 12 after tax cost of debt is 8 and tax rate is 40 What is the company s WACC 9 60 11 2 10 67 10 56

5 A Ferris wheel in Niagara Falls has a diameter of 30 metres and one revolution takes 3 minutes to complete a Sketch a graph showing the height of a rider above the ground as a function of time if the rider gets on at a height of 1 metres at t 0 minutes b Determine the equation which expresses the height of the rider with respect to time Show all

4 Sketch the graph of the polynomial function f x that has a zero at 2 of order 3 a zero at 4 order 2 two zeros of order 1 at 1 and 5 and a positive leading coefficient This function also passes through the point 3 16 a Determine the specific equation for f x in factored form

3 Evaluate each of the following Answers and solutions must be expressed as exact values no decimals a 2log2 2log5 2log3 log 25 b

A laboratory designed a radio telescope that had a diameter of 280 ft and maximum depth of 46 ft a Write an equation of a parabola that models the cross section of the dish if the vertex is placed at the origin and the parabola opens up b The receiver must be placed at the focus of the parabola How far from the vertex should the receiver be located a The equation of the parabola is Simplify your answer Use integers or fractions for any numbers in the equation b The receiver should be located at approximately ft above the vertex Type an integer or decimal rounded to the nearest tenth as needed 53

Since cos t is an even function rewrite cos t as cos t cos t

Fill in the table Transformed Function Mapping Notation Amplitude Period Horizontal Axis Phase 2 COS 7 x 1 3 g x 2 cos cos

the stant as of the on b Follow the seven step strategy and use the slant asymptote to graph the rational function f x x x 6 X 3 a Select the correct choice below and if necessary fill in the answer box to complete the choice A The equation of the slant asymptote is Type an equation B There is no slant asymptote onal b To graph the function first determine the symmetry of the graph of f Choose the correct answer below neither y axis symmetry nor origin symmetry v axis symmetry

f For the functions f x 2 x and g x x 2x8 find f g f g fg and Determine the domain for each function g f g x Simplify your answer What is the domain off g Select the correct choice below and if necessary fill in the answer box to complete your choice A The domain off g is Use a comma to separate answers as needed The domain of f g is OC The domain off g is B fog x Simplify your answer What is the domain of fg Select the correct choice below and if necessary fill in the answer box to complete your choice OA The domain of fg is Type your answer in interval notation Use a comma to separate answers as needed The domain of fa is

1 Ethan throws a toy soldier with a parachute into the air from a balcony The path of the soldier can be modelled by h t 5 7t 18 where the height h t is in metres and the time t is in seconds a When will the soldier hit the ground 2 marks b How long will the soldier be above 15 m 2 marks

Suppose x 3 is the only critical point for f x If the derivative of the function f x is negative on infinity 3 and positive on 3 infinity what must be true about f a Has a minimum at 3 b Has a maximum at 3 c Has an inflection point at 3 d None of the above

oes either the domain and or range of f x x need to be restricted in order to find an inverse function Explain why or why not

1 Consider the data below for a car tire with a leak K Minutes after the leak began 0 5 10 Pressure of air in the tire in kilopascals kPa 400 335 295 15 255 20 225 25 195 30 b Estimate the instantaneous rate of change at 5 minutes using a surrounding interval 170 a Calculate the average rate of change over the 30 minute interval Explain the meaning of this rate using proper units

5 Use the graph to find the following limits K a lim f x x 00 b lim f x c lim f x x 0 d lim f x x 0 e limf x x 0 34 16 12 8 4 0 18 f x 12 16 X 2x 8x 4

4 Find the equation of the derivative for the following function Also find the instantaneous rate of change for the function when x 2 and x 3 K a f x 4x 1

1 Use the graph of y f x to graph the function g x f x 4 2 B 6 y f x Ay 6 8 ob 6 44 a 2 4 6 2 X

4 Andy bought an airplane and wanted to determine the most efficient power setting She kept records on the range of the aircraft in kilometers starting with a full tank of fuel for a number of power settings in revolutions per minute rpm The results are T 15 shown below Power Setting rpm Range km 1500 1600 1700 1800 1900 649 695 733 763 785 a Does the Power Setting show equal intervals b Calculate the first differences What does it imply about the rate of change constant increasing decreasing c Calculate the second difference What does it imply

Trish invests 6 000 in her IRA in a bond trust that pays 10 interest compounded semiannually Sean invests 6 000 in his IRA in a certificate of deposit that pays 9 7 compounded continuously Who has more money afte years Trish or Sean After 20 years Trish will have Round to the nearest cent as needed

Solve homogeneous equation x 2 y xy y 2

x 2m 6 3m O EL 2 Ar 2m 15 14 09H KICKIN 11M 44 15 15 15 6 Use the given graph of f x sinx to graph g x cscx Complete the table of values as well APP f x g x 1 1

Determine whether the series is convergent or divergent use ratio test or root test 1 n 1 n n 1 2 1 1 n 1 3 2 n n n 4 45 TL4 n 4 00 1 100n e4n 5 n 3 n 2 pls show neat and whole solution

Find the Taylor series for f x 8x 1 9x Give the interval of convergence What is the Taylor series for f x OA 8x 8 9x 8 92x 8 9 x4 1 18 9x 1 B 9x 9 8x 93 8 x 94 8 x 1 1gn 1 8x 14 OC 9x 9 8x 9 8 x 9 83x 1 9 8 x 1 D 8x 8 9x 8 9 x 8 9 x 1 8 9 x The interval of convergence is Type integers or fractions

3x 3y 6 3x 3y 6 of the lines in the system of equations by substitu

Solve the equation 2x 2 y 2xy 20 0 Solve the differential equation y 4y 3y e 3x x 1 Solve the equation x d 2y dx 2 2 dy dx 2 dy dx

What type equation is y q x y r x y f x Show that yp e 2x is a particular solution to y 2y 3y 5e 2x and find the solution to the IVP y 2y 3y 5e 2x y 0 5 y 0 2 Find the general solution of the given equations a y 4y 5y 5x 1 b y 00 y 0 x 2 2x 1

Solve x In x y y 2 In x using integrating factors Solve Bernoulli Equation y 3 x y x 2 y 2 X 0 Solve homogeneous equation x 2 y xy y 2

7 Write as a single exponent 5 3 6 pts

A 2 Match each graph in the table with the graph of its inverse A B or C Then write an equation for each function K Graph 2 0 2 x 2 Equation 2 0 24 Equation of inverse 2 x Letter of Graph of Inverse y 4 2 0 2 y 4 N 0 N x y 4 2 0 2 2 to x 20 0 2 x

each graph with its equation Lastly complete the table K a f x 2 x int y int Domain Range Asymptote f x 10 9 4 4 3 2 x int y int Domain Range Asymptote 1 10 9 8 7 6 5 4 3 2 4 0 1 2 3 4 5 6 7 8 9 10 2 3 f x OIL 5 8 9 10

Differentiate the function g x g x 1 2x3 3x 1 3 4

Assume that u satisfies the mean value property That is for all x y R 27T 1 7TR f 0 0 u x y u x rcos 0 y rsin 0 rd0dr

Verify the given linear approximation at a 0 Then determine the values of x for which the linear approximation accurate to within 0 1 Round your answers to three decimal places 1 x 1 X X x

The price of tomatoes is 1 6 lb How many would you need to buy 9 9 lb

If your recipe calls for 3 eggs and 7 0 cups of flour to make 24 0 bagels how many bagels will you be able to make if in your bakery all you have available are 53 eggs and 104 1 cups of flour

Referring to the following table for the question Taxable Income Marginal Tax rate 0 10 000 10 10 000 30 000 15 over 30 000 20 What is the average tax rate if the taxable income is 41 200 Hint enter your answer in 2 decimal places Do NOT enter the sign For example 36 546 shc be entered as 36 55

Students in the new MBA class at a state university have the specialization profile given below Find the probability that a student is either a finance or a marketing major Are the events finance specialization and marketing specialization mutually exclusive If so what assumptions must be made Finance 89 Marketing 38 Operations and Supply Chain Management 74 Information Systems 59 Select the correct choice and if necessary fill in the answer box to complete your choice OA Since the outcomes are mutually exclusive the probability that a student is either a finance or a marketing major is Round to two decimal places as needed OB Since the outcomes are not mutually exclusive the probability cannot be found using only the information given OC Since the students may or may not be allowed to have multiple majors it is not known if the outcomes are mutually exclusive If it is assumed that the majors are not mutually exclusive then the probability that a student is either a finance or a marketing major is If it is assumed that the majors are mutually exclusive then the probability cannot be found using only the information given Round to two decimal places as needed No assumptions need to be made OD Since the students may or may not be allowed to have multiple majors it is not known if the outcomes are mutually exclusive If it is assumed that the majors are not mutually exclusive then the probability that a student is either a finance or a marketing major cannot be found using only the information given If it is assumed that the majors are mutually exclusive then the probability is Round to two decimal places as needed

A hat contains 4 marbles one orange one green one red and one yellow Two marbles are selected at random without replacement from the hat Compleu O Click here to view diagram d Click here to view diagram b O Click here to view diagram c O Click here to view diagrama List the sample space Choose the correct answer below A OG OR OY GO GR GY RO RG RY YO YG YR OB O G R Y OC 00 OG OR OY GO GG GR GY RO RG RR RY YO YG YR YY OD OO GG RR YY c Determine the probability of selecting exactly 1 green marble The probability is Simplify your answer d Determine the probability of selecting at least 1 marble that is not green The probability is 1 Simplify your answer e Determine the probability of selecting no red marbles The probability is GITE

You have a balance of 9900 for your tuition on your American Express credit card Assume that you make no more charges on the card Also assume that American Express charges 11 APR and that each month you make only the minimum payment of 4 of the balance Find a formula for the balance after r monthly payments Give an exact solution Use symbolic notation and fractions where needed balance after r months S

1 What is the remained when x4 4x 2x 3 is divided by x 1 Do not divide Support your answer with an explanation TI

8 Find an equation for the following graph TI 3 2 2 3x

6 Solve the following polynomial inequality App a 2x 1 x 2x

7 Find the equation for the family of quartic polynomials that have real roots of 3 order 2 and 2 2 APP

Write the original maximization linear programming given the following initial simplex tableau S1 S2 S3 Z 1000 X1 X2 X3 1 2 3 2 3 1 2 5 6 1 0 0 0 48 4 0 1 0 0 82 2 0 0 1 0 56 0 1

Thinking 6 marks a Sketch a graph for the polynomial function You must include all key features of polynomial graphs Indicate a scale f x x x 2 x 6 x 4 x 6 x 3 T4

X 3 2 1 O 1 2 IN 3 y 110 30 The function is cubic linear quadratic quartic 30 110 61 2 61 d

The function y x 2x 3 3x 4 3 is negative on the intervals Oxe and x 0 00 Oxe fo and re XE Ox and xc 1 XE XE 8 Oxef 00 and xe 0 3

The function y x 4 x 7 x 3 3 is negative on the intervals 3 4 and 7 infinity negative infinity 3 and 7 infinity negative infinity 3 and 4 7 3 4 and 4 7