Functions Questions and Answers

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

By expanding e in a Maclaurin series and integrating term by term show that My t Since f x is a probability distribution Using the definition of the Write the second term of the product ef x using the Maclaurin series tx f x as t 00 S 00 S x 10x dx fju 00 CE f x dx 1 expected value Write the third term of the product e f x using the Maclaurin series 00 GEIXE 2 1x dx 1 2 of a continuous random variable X and then moving all constants outside the integral the integral of the second term can be rearrange

1q046P The table of values represents points on the graph of a quadratic function 2 1 12 7 What are the coordinates of the graph s vertex What is the general form of the function s equation f x x Y 0 1 2 434

The function graphed to the right is of the form y a sin bx or y a cos bx where b 0 Determine the equation of the graph y Type an expression using x as the variable COLL 2 N 34 3x NA 2 2x

7 points Use transformations to graph f x 4 1 x show all steps and then graph its inverse if possible

The graph of f x is given below Identify the correct graph of g x 2f x 4 3

f x is transformed from y 2 by horizontally stretch by a factor of 2 shift 5 units to the left reflect about the x axis and shift 3 units up Find the equation for f x f x 2 x 5 3 O O f x 2 x 3 5 Of x 5 f x 5 f x 5 3 f x 5 3

The graph of f x is given below 0

The following table contains financial information for Trumpter Inc before closing entries Cash Supplies Prepaid Rent Salaries Expense Equipment Service Revenue Miscellaneous Expenses Dividends Accounts Payable Common Stock Retained Earnings 13 100 6 000 3 800 5 000 65 900 28 000 20 100 4 000 3 100 66 100 20 700 What is the amount of Trumpter s total assets

1 1 point To graph f x x 2 4 by transformation we do the following Order the steps in the correct order Begin 1 2 3 4 End Graph the parent function y Reflect about the x axis Shift 2 units to the left Shift 4 units down

8 Basic reciprocal function f x 8 Answer the following and then graph the function a What is the domain of this function b What do you think is the range of this function c Choose at least two negative numbers and two positive numbers for the values of x x y x 10 5 Describe the features of the graph 5 5 10 Cr

7 Basic cube root function f x x 7 Answer the following and then graph the function a What is the domain of this function b What do you think is the range of this function c Choose two negative numbers 0 and two positive numbers for the values of x y x X 10 Describe the features of the graph 5 K LO 5 5 10 5

Find the slope of the line graphed below ee 1 4

Describe f x O O the the feature of the graph of the following function Domain Range 00 00 The graph is an increasing function As x values gets smaller and smaller y values gets smaller and smaller As x values gets larger and larger y values gets larger and larger Domain 0 U 0 0 Range 0 0 U 0 0 The graph does not cross the x and y axis Domain 0 00 Range The graph is a straight line with slope of 1 and y intercept 0 0 Domain 10 00 Range 0 00 The graph is half of a parabola lying on its side

1 iven f x and g x what is What is the domain of T 3 3 r 9 Of x x 2 3 T 1 0 x 2 2 3 2 I Of x 2 3 I 3 Of x x 2 3 z domain 3 U 3 0 Of r 7 20 3 2 domain 2 U 2 3 U 3 0 domain 2 U 2 domain 2 U 2 3 U 3 0 domain 0 2 U 2 3 U 3

096P The radius r in inches of a spherical balloon is related to the volume V by r V Air is pumped into the balloon so the volume after t seconds is given by r V t V t 16 14t a Find an expression for the composite function r V t To enter type pi To enter a cube root use a fractional 1 3 exponent type 3V 4T b What is the exact time in seconds when the radius reaches 12 inches

OSCAGC03s04q066P Use the function values for f and g shown in Table 4 to evaluate fog 2 fog 2 x 3 f x 11 g x 8 2 1 9 7 3 0 Table 4 0 1 5 3 1 0 2 1 3

SC035040068P Use the function values for f and g shown in Table 4 to evaluate gof 2 3 2 1 9 3 H f z 11 g z 8 7 0 0 3 1 Table 4 1 2 1 3 30 3

More on Polynomials Question 5 Which statement is true about the function shown here Select one This function is neither even nor odd This function is even This function is both even and odd This function is odd It is impossible to tell whether this function is even or odd 4 2 2 4

Find an equation of the form y ab csin a b X C y To fit the data 06 1 26 28 96 3 382 72 x that fits the data below

Problem 5 20 pts No calculators Using the Disc or Washer method only find the exact value of the volume of s solid obtained by rotating the region enclosed by y x and x y about y b c Sketch the two curves on the same graph and shade in the region between them Show calculations for intersection points Sketch the 3D volume that results when you rotate the shaded area from part a about y 1 Draw a typical disc or washer on this 3D sketch Determine an expression for dV as shown in lecture State which variable is queen variable and give a brief explanation

ose the correct answer below 9P2 3 2Pg C 2Cg 5 9C

Find the area of the triangle below 12 m 6 m 17 m 7 5 m

What ordered pair is shown plotted on the rectangular coordinate plane below 10 17 10 S 10 10

Find the value of 24 in 36 in 12 in 8 in

bability of selecting a bird or an even number is ninteger or a simplified fraction a 7 X P 3 30 2 37 12 2 37

K If P A or B 0 8 P A 0 4 and P A and B 0 15 find F P B Simplify your answer Type an integer or a decimal

ne formula for finding the probability of event A or event B is P A or B

An outboard motor has an initial price of 1 250 A service contract costs 300 for the first year and increases 130 per year thereafter The total cost of the outboard motor in dollars after n years is given by C n 1 250 250n 50n where n 1 Complete parts A through C A Write an expression for the average cost per year C n for n years C n B Graph the average cost function found in part A Choose the correct graph below OB OA Ay 4 500 0 0 n 20 G Ay 4 500 0 0 n 20 O C 4 500 Ay 0 n 20 OD 4 500 Ay 0 0 C When is the average cost per year minimum This time is frequently referred to as the replacement time for this piece of equipment The average cost per year is minimum after years n 20 LV

Enter the number that belongs in the green box 96 13 25 Round to the nearest hundredth Enter

The accompanying data for the S P 500 provides open high low and close values for the S P index over a period of time Complete parts a through c below Click the icon to view the S P Index a Enter any day from July to August 2013 within the range of the data in cell G2 Use a MATCH function in cell G3 to find the row in the database that corresponds to this day Day 1 representing August 1 2013 has been added to cell G2 What MATCH function should be used in cell G3 to find the row in the database that corresponds to this day D A 1 S P 500 Data 2 3 4 5 6 B 22 23 24 C E F Day Database Day July to August 2013 Open High Low Close row 1694 41 1697 61 1690 67 1695 53 1696 63 1698 78 1691 13 1692 39 1696 06 1698 381682 57 1685 94 G MATCH G2 A4 A23 1 MATCH G2 A4 E23 1 MATCH G3 B4 B23 0 Day July to August 2013 High Close 1697 61 1690 67 1695 53 Open 22 1694 41 23 1696 63 1698 78 1691 13 1692 39 24 1696 06 1698 38 1682 57 1685 94 25 1685 21 1690 94 1680 07 1690 25 26 1687 31 1691 85 1676 03 1691 65 29 1690 32 1690 92 1681 86 1685 33 30 1687 92 1693 19 1682 42 1685 96 31 1 2 5 6 1687 76 1698 43 1684 94 1685 73 1689 42 1707 85 1689 42 1706 87 1706 1 1709 67 1700 68 1709 67 1708 01 1709 24 1703 55 1707 14 1705 79 1705 79 1693 29 1695 3 1695 3 1684 91 1693 35 1700 18 1688 38 1696 1 1699 42 1686 02 1688 37 1691 49 1683 35 1690 65 1696 81 1682 62 1697 37 1690 91 1697 48 1691 42 1689 47 1694 16 1685 39 1693 88 1695 52 1684 83 1679 61 1679 61 1658 59 1661 32 16 1661 22 1663 6 1652 61 1655 83 7 8 9 12 13 14 15 Low

vert the accompanying database to an Excel table to find The total cost of all orders The total quantity of airframe fasteners purchased he total cost of all orders placed with Manley Valve Click the icon to view the database The total cost of all orders is Supplier 1 2 Hulkey Fasteners 3 Alum Sheeting 4 Manley Valve 5 Fast hyphen Tie Aerospace 6 Fast hyphen Tie Aerospace 7 Steelpin Inc 8 Fast hyphen Tie Aerospace 9 Manley Valve 10 Steelpin Inc 11 Durrable Products 12 Fast hyphen Tie Aerospace 13 Fast hyphen Tie Aerospace 14 Steelpin Inc 15 Hulkey Fasteners 16 Manley Valve 17 Hulkey Fasteners 18 Steelpin Inc 19 Steelpin Inc 20 Alum Sheeting 21 Hulkey Fasteners 33 22 lain los Item Description Airframe fasteners Airframe fasteners Hatch Decal Shielded Cable ft Shielded Cable ft Shielded Cable ft Shielded Cable ft Machined Valve Bolt nut package Pressure Gauge O Ring Shielded Cable ft Shielded Cable ft Electrical Connector Pressure Gauge Hatch Decal Electrical Connector Bolt nut package Control Panel Electrical Connector Flactrical Connector 4 25 3 75 1 05 1 05 1 05 1 1 1 05 655 5 3 75 90 2 45 1 05 1 1 25 100 5 0 75 1 65 3 75 255 1 25 11 19500 12000 560 23000 23500 17500 23500 125 4250 100 1300 22500 18200 5600 80 600 4500 4200 506 5500 4850 82875 45000 588 24150 24675 19250 24675 81937 5 15937 5 9000 3185 23625 18200 7000 8040 450 7425 15750 129030 6875 5335

Plot the intercepts to graph the equation 2x 3y 6 Use the graphing tool to graph the equation Use the intercepts when drawing the line If only one intercept exists use it and another point to draw the line Click to enlarge graph 404 18

Add these Binary numbers 10101010 101 O 10101111 O 11110101 O 01010101 O 101 4

11 1 point Which equation can be used to model the graph of the function shown a y sin 2x 3 b y 2 sin x 3 60 120 180 240 3000 360x c y sin 2x 3 d y 2 sin x 3

13 1 point The asymptote of the function f x b is a the y axis b the x axis c x b d y b

6 2 points Determine the monthly payment for a five year loan on a 19000 vehicle at 7 per year compounded monthly a 265 39 c 444 14 d 376 22 b 328 80

7 1 2 points The roots to the nearest hundredth of y x x 1 are 1 83 and 3 83 b 1 83 and 3 83 c d 1 83 and 3 83 1 83 and 3 83

1 x 2x x x 1 3 Let f x a Analyze lim f x and lim f x X48 x 00 b Does f have a slant asymptote If so write the equation of the slant asym

Find the total cost function C x in thousands of dollars if the marginal cost in thousands of dollars per unit at a production level of x units is C x c 0 20 COCO Which of the following explains how to find C x the total cost function if the marginal cost at a production level of x units is C x A To find the total cost function evaluate the indefinite integral of the marginal cost and apply the initial conditions c 0 20 Therefore C x Type an exact answer B To find the total cost function evaluate the derivative of the marginal cost and apply the initial conditions c 0 20 Therefore C x 8x 5 0 x 4 and fixed costs are 20

Gate A 0 Symbol B 0 D Truth Table output Gate Symbol Truth Table A B 0 0 output

What is the expected payout or value from playing a game with the listed prizes and probabilities in the table Outcome A B C 1 85 2 15 5 60 6 00 Probability 25 35 40 Prize Amount 3 2 1

Which description best represents the correlation coefficient sum of the squared deviations square root of the average of the squared deviations equation of the line of best fit measure of fit of the data to a regression

Which inequality is graphed below do 7 6 x 4 x 4 x 4 x 4 5 4 20 2 1 0 2 3

A ball is thrown in the air from the top of a building Its height in meters above ground as a function of time in seconds is given by h t 4 9t 20t 7 How long does it take to reach maximum height Round your answer to the nearest tenth It takes seconds for the ball to reach its maximum height

er progress bar may be uneven because questions can be worth more or le Which value of a will make the following equation true 59 53 O No value of a will work O 125 a 0 a 3 a 4

OSCAGC03s04q078P Use the functions f x 4x g f 4 f g 4 3 and g x 4x 3 and g x 3x 3 to evaluate the following

OSCAGC03s04q012aP Use the given functions to find g x f x x 4 and g x x 3 g x

Siven f x and g x x 81 find Give your answer as an expression

Are the two matrices similar If so find a matrix P such that B P 1AP If not possible enter IMPOSSIBLE 1 0 0 A 0 3 0 002 P B 300 0 1 0 002