Functions Questions and Answers

6 Write an equation for the function that results from the given transformations APP The function f x x4 is compressed vertically by a factor of stretched horizontally by a factor of 2 reflected horizontally in the y axis and translated 1 unit up and 4 units to the left

Write the following complex number in rectangular form 4 4 3 3 4 COS isin 4 4 COS isin 3 0 1 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type your answer in the fo Rationalize all denominators

The sound produced by touching each button on a touch tone phone is described by the equation below where I and h are the low and high frequencies in the figure shown The touch tone phone sequence for Mary Had A Little Lamb is 3212333 222 399 3212333322321 Many numbers do not appear in this sequence including 0 You accidentally touch 0 for one of the notes y sin 2 lt sin 2sht t is time in seconds a Enter the sound produced as the sum of sines AY ABO N EMA 200 WUS UNO S EG 697 770 852 941 Low frequencies High 1209 1336 1477 frequencies

3 Determine the polynomial function whose graph passes through the following points 2 4 3 6 5 10

4 Use finite difference to determine the degree and value of the leading coefficient for eac polynomial function App 3 2 1 0 1 2 3 124 41 8 1 4 31 104 247

7 Use the given graph to state K a x intercepts b number of turning points c least possible degree d any symmetry present even or odd function e the intervals where f x 0 N

5 Lida s car has a 55 L tank How many gallons of gas can she fill the tank with if it is completely empty

1 point List all real values of such that f x 0 If there are no such real x type DNE in the answer blank If there is more that one real x give a comma separated list e g 1 2 f x 8 x 20 1 x 17

1 point Find a possible formula for the function graphed below Assume the function has only one x intercept at the origin and the point marked on The the graph below is located at 2 asymptotes are x 2 and x 1 Give your formula as a reduced rational function f x formulas X 2 y x 1 2 1 2 help X

1 point Leave any unneeded answer spaces blank f x notation is f x The domain of the function f x in interval 8x 10x 67x105 2x 19x x 90 Enger the root s of f x as a comma separated list list of values f x has one hole at the point f x has vertical asymptotes when x is enter a comma separated f x has a horizontal asymptote at y

12 22 sure your grapn snows all intercepts and exnidits proper end behavior Then enter the letter corresponding to the correct graph next to each formula for P x A 3 C D E 1 P x x 2x 3 2 P x 2x x x 3 P x x 1 x 3 4 P x 3x x 2 x 3 5 P x x 3x 4x 12 N Not Secure webwork2 columbiacollege bc ca

1 point The graph below is a polynomial function in the form f x x a x b x c Find suitable unique real numbers a b and c that describe the graph 8 Answer a and c 1 0 8 b Note You can click on the graph to enlarge the image

en science class Richard learns that petrol has a boiling point of 203 Fahrenheit His teacher asks him to convert this emperature to degrees Celsius What is the boiling point of petrol in degrees Celsius 307 8 C O 397 4 C O 95 C 130 6 C

1 point 24 18 12 6 5 4 3 2 1 6 6 12 18 24 1 2 3 5 6 X Determine the equation of the polynomial x of minimum degree whose graph is shown above Write your answer in factored form f x Help Click here for help entering formulas

1 point Find all zeros and vertical asymptotes of the rational function f x If there is more than one answer enter your answers as a comma separated list If there is no solution enter NONE Do not leave a blank empty a The function has x intercept s at x help numbers x 1 x 1 b The function has y intercept s at y help numbers X c The function has vertical asymptote s when help numbers Y d The function has horizontal asymptote s when help numbers

Next Problem 1 point The polynomial of degree 3 P x has a root of multiplicity 2 at x 5 and a root of multiplicity 1 at x 5 The y intercept is y 75 Find a formula for P x P x

THEOREM 7 4 1 Derivatives of Transforms If F s L f t and n 1 2 3 then L t f t 1 n dn F s dsn valuate the given Laplace transform Write your answer as a function of s L 6t cos t 2 2 1

5 Write down the equation of a line that is parallel to a y 3x b y 2x 3 dy x 2 e x 8

Find the inverse Laplace transform O L OL OL S 25 59 s 27 5 45 13 2 L 35 22 5 4

symbol s is used to indicate the standard deviation of a symbol s is used to indicate the standard deviation of a statistic sample piece of data

company held a contest and the following information was included in the fine print PRIZE A B C D TOTAL WIN WIN NUMBER OF PRIZES 13 52 520 28 900 29 485 PROBABILITY OF WINNING INDICATED PRIZE 0 000005 0 00002 0 0002 0 010886 0 011111 Read this information carefully and calculate the expectation to the nearest cent for this contest Assume that Prize A is 90 000 Prize B is 1 000 Prize C is 200 and Prize D

Use the sample space shown in the figure to find the probability for the experiment of rolling a pair of dice Enter the probability as a fracti P eight THE 36 WAYS DICE CAN ROLL

Example 2 9 John Dilcher is paid an hourly rate of 18 50 per hour and he worked 49 hours this week His gross pay is 40 hours x 18 50 740 00 regular earnings 249 75 overtime earnings 989 75 9 hours x 27 75 18 50 x 1 5 Total gross pay John Porter is an hourly employee of Motter Company located in New York City This week Porter had to travel to the company s regional office in Albany He left Sunday at noon and arrived in Albany at 3 00 P M During the week he worked his normal 40 hours in the Albany office Monday through Friday 9 A M to 5 P M In addition he attended the company s mandatory 4 hour work training session on Wednesday evening Porter s hourly rate of pay is 12 10 per hour Round the overtime rate to two decimal places and use the rounded amount in subsequent computations Round the final answers to the nearest cent a Porter s overtime earnings for the week are b Porter s total earnings for the week are

tnEN Discuss the convergence or or divergence of the improper integrals fofi 160 e 15 ma

Which two of the expressions below are equivalem x 2 4 32 A

is Find the consumer s surplus if the demand function for a particular beverage given by D 9 2000 and if the supply and demared are in equilibrium 2q 5J The consumers surplus is Round to the nearest cent as needed

4x 1 12 3 3 x 9 9 Graph the solution Use the tools to enter your answer 19 3 113

5 5 10 5 50 desmos Determine an equation in factored form for this parabola

To ty 8 4 2 10 4 2 0 2 4 6 8 10 y x 6x 2 4 6 8 10 Where are the zeros and minimum value located for this quadratic relation zeros 0 6 minimum 9 zeros 0 6 minimum 11 zeros 0 0 minimum 9 zeroes 0 0 there is only a maximum value

6 8 7 6 4 3 2 1 5 4 3 2 1 1 2 1 2 3 4 5 6 O Write an equation in the form y c a sec b x d or y c a csc b x d for the func graphed above

Where is the vertical asymptote of g x 3 log x 2 5 a x 1 b x 0 O c x 2 d x 2

What is the domain of the function shown 0 15 Oa x R Ob x ER x 0 Oc x R x 0 Od x R x 0 15 20 25 30 35 4

Given the Boolean matrices M and N as shown here select the matrix that equals M v N M 010 111 N 110 000

Determine the equation of the inverse of y a y x log b y log Oc y log Od y P 3

2 A function f x has the following properties a There is a hole at x b There are two zeroes One zero occurs when x c The equation of the horizontal asymptote is y d The equation of the vertical asymptote is x e The function passes through the point 0 2 Determine the equation of the rational function and state the 2nd zero 5 marks

The table below shows some input output pairs of two functions f and g that agree for the values that are given but some of their output values are missing t f t g t 0 0 0 15 0 5 0 5 30 45 1 3 1 3 60 2 2 75 2 7 2 7 90 105 4 4 Graph both functions and explain from the graph why f is invertible and g is not Come up with two real life situations that f and g could be representing Find and interpret the value f 4 in terms of these contexts 120 Complete the table in a way so that f could be invertible and so that g is definitely not invertible

Given the following two functions shown below The graph in green is y f x and the graph in blue is y g x 15 14 13 12 11 10987 2 5 0 556 7 6 marks 6 5 3 2 3 4 5 6 Determine the intervals on x where f x g x Your solution must be entirely algebraic Simply reading the intervals off of the graph will result in a mark of zero Note The horizontal asymptote for y f x is y 1 and the vertical asymptote is x 7 The horizontal asymptote for y g x is y 1 and the vertical asymptote for y g x is x 2

16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 3 5 6 7 8 9 10 11 12 The curve above is the graph of a sinusoidal function It goes through the points 12 0 and 2 0 Find a sinusoidal function that matches the given graph If needed you can enter T 3 1416 as pi in your answer otherwise use at least 3 decimal digits f x

Question 1 1 point State the range of f x 1 f x 3x 4 O E a y R y 0 Ob ye Ry Od ye Ry 0

x r x s A reciprocal of a quadratic function has the form f x k R k 0 The graph is shown as below If r 1 s 2 and the minimu value of f x is 0 8 over the interval 1 x 2 Determine the value of k rounded to one decimal place Show your work by attaching a file S This graph is not to be scaled h

A rational function has the form f x ax 1 2x d determine the value of a and if f x has a horizontal asymptote at y 2 and a vertical asymptote at 1 2 Enter the value of a and d in box 1 and 2 respectively x Blank 1 Blank 2 A N

Which statements are correct for the function f x The range of the function is R y E R The function is increasing over its domain The graph of the function has a hole PUROR x x 6 x 2x 3 The graph of the function has a horizontal asymptote at y 1

10 Following is the sign chart of a factorable rational formula with its roots asymptote and their orders Write down a any factored rational formula with the following given sign chart and sketch its graph 0 asymptote ord 1 ord 2 ord 1 root

For the following questions use the compound interest formula A t P 1 2 After a certain number of years the value of an investment account is represented by the expression 10250 1 0 03 4 a What is the value of the account rounded to the nearest dollar Use the symbol in your answer b What was the initial deposit made to the account Use the symbol in your answer c How many years had the account been accumulating interest 10250 13 years 52

Find the magnitude and direction of the vector 4 2 4 2 w Select the correct answer below O 8 0 135 Ow 16 0 135 Ow 16 0 315 Ow 8 0 225 Ow 16 0 225 O 8 0 315

5 t 5 grapi 5 4 3 2 S 7 3 No w 2 2 345 5 5 3 2 5 4 3 2 1 2 par 345 4 5 4 3 2 Pe 1 2 3 4 5 1 2 3 tion Not all equations will be used All graphs shown a b C d e a t t cos t ly t t sin t x t t y t 1 x t 2 cos t y t sin t x t t t y t x t t y t t

2 tx By expanding in a Maclaurin series and integrating term by term show that Mx t f x dx 1 t 2 e e Expand ex in a Maclaurin series ex 1 tx 22 2 tx Write the first term of the product ef x using the Maclaurin series f x 88 TH

Which of the following are graphs of polynomia functions check all that apply K

By expanding in a Maclaurin series and integrating term by term show that Mx t 1 x dx 1 t 1 x dx 1 l 2 Write the third term of t 1 x 2 21 3 Using the definition of the expected value of a continuous random variable X and then moving all constants outside the integral the integral of the second term can be rearranged as t f x f x dx f x Using the definition of 80 the rth moment about the origin the expected value 00 the moment generating function rearranged as 1 x dx 2 00 CRECE of a continuous random variable X and then moving all constants outside the integral the integral of the third term can be

The moment generating function of the random variable X having a chi squared distribution with v degrees of freedom is Mx t 1 2t show that the mean and variance of the chi squared distribution with v degrees of freedom are respectively v and 2v Express the mean of X u in terms of a moment about the origin of X P This moment about the origin can be found by evaluating My 0 For any value of t the derivative identified in the previous step is v 1 2t Evaluating this expression at Simplify your answers yields Thus the mean of the chi squared distribution with v degrees of freedom is v Use this moment generating function