Functions Questions and Answers

Question from Real Analysis subject in University Answer using working out please In 1969 Armstrong Aldrin and Collins became the first humans on the moon They lifted off from Cape Canaveral did a loop of the earth then headed for the moon where they landed 102 hours 45 minutes and 40 seconds later During that time of course the earth was busily rotating and the moon was busily orbiting and so forth so it is very difficult to describe exactly how far they were from Cape Canaveral or from the moon at most points in time during their trip Prove that there was a moment during the trip where they were exactly the same distance from Cape Canaveral as they were from their eventual landing site on the moon You can assume that the distance between two given objects is a continuous function of time

lackberry strawberry kiwifruit e the answer that lists all of the subsets of blackberry strawberry kiwifruit blackberry strawberry kiwifruit blackberry strawberry blackberry kiwifruit strawberry kiwifruit blackberry strawberry kiwifruit blackberry strawberry kiwifruit blackberry strawberry blackberry kiwifruit strawberry kiwifruit 0 blackberry strawberry kiwifruit blackberry strawberry blackberry kiwifruit strawberry kiwifruit 0 blackberry strawberry kiwifruit blackberry strawberry blackberry kiwifruit strawberry kiwifruit blackberry strawberry kiwifruit

moose the correct answer below A AUB c f g s t B AUB m p y OC AUB cf g m p s ty D AUB a c d f g m p s tv x y AXTON

red C red pink brown Jue or false is raise give the reason SITE se the correct answer below This statement is false The set red is not an element of the second set This statement is false The second set is a proper subset of the first set not the other way around This statement is false No set is a proper subset of itself This statement is false The element red is not an element of the second set E This statement is true

Venn diagram shown to list the set B n C in roster form 13 10 S 12 14 15 18 BNC Use ascending order Use a comma to separate

Venn diagram shown to list the set B in roster form 10 11 13 17 14 18 Use ascending order Use a comma to separate

K Complete DeMorgan s law a AUB b An B a AUB A B b A n B

3 2x 1 3x 5x x 1 x 3 expand Simplify

rectangle has width x 1 length Vx 1 and diagonal 6 extraneous roots Solve for x and check for

6 Determine the inverse of the function y 2 log4 x 2 T1 mark

Consider the piecewise function with a point discontinuity at 3 1 y 57 5 y2 4 3 or 3 3 2 all real numbers all rational numbers 1 3 2 N M 3 1 2 What is the domain of the piecewise function 51 1 2 3 4 5 X

Consider the two linear functions f x and g x Several values of f x are given in the table and g x is graphed on the coordinate plane 5 b x 1 f x 2 m 2 1 2 1 2 3 4 1 6 y H What is the sum of the slopes of the two functions 3 10 2 3 10 24 4 5 X g x

Consider the function Which statement is true A The function has 0 real solutions because the function never crosses the x axis The function has 1 real solution because the function crosses the x axis once B The function has 2 real solutions because the function crosses the x axis twice D The function has 3 real solutions because the function crosses the x axis three times C y x x x 1 b

The graph shows the number of gallons of water in a bathtub y as a function of time x Number of Gallons 60 50 40 30 20 10 y 16x 2 5 0 1 2 3 4 5 Time in minutes For 0 x 5 which function best represents the graph y 16x40 y y 16x 40 y 16x 2 5 6

Find y when y O 2e x 2e O2e 1 e x X 2 e x 1 e a 4e x 3e x 2x 4e x 3e x 1 e x 4e x 3e x 1 e x O2e 4e 4e x 3e x 1 e x

5 Find y when y Ox 2 sin x 2x COS X O x x cos x 2 sin x x sin x X Incorrect x cos x 2 sin x sin x Ox x cos x 2 sin x sin x O x x sin x 2 cos x sin x

5 Which one of the following is the correct sign diagram for the derivative y of the function y x 2x O O O 1 0 1 1 11 0

The graph of y x is the solid black graph below Which function represents the dotted graph 10 9 8 7 6 5 4 3 2 1 1 Oy x 4 Oy x 4 1 1 1 10 9 8 7 6 1 S 23 4 5 6 7 8 9 10 1 N 3 5 6 Oy x 4 Oy x 4 8 9 10 Submit Answer

5 Write a third degree polynomial function with rational coefficients that has roots 0 and 2 7 2 ifn 1

For each tranformed function g x find the parent function f x the transformation parameters a b h k the mapping notation a transformation table with three points a sketch and the domain and range of g x a g x 2 3 x 4 1 Transformed Function Parent Function Mapping Notation Transformation table f x 1 KU f x 1 KU 1 5 A b g x 13 Cl 2 x 5 7

b Determine if each relation is a function If it is not describe two points that demonstrate it is not a function State the domain and range i 1 3 1 3 2 4 7 7 Function Domain Range 1 Function 2 Domain Range 3 2 1 0 O 1 2 3 1 5 KU ii 1 3 1 2 0 0 99 1 1 5 KU Function Domain Range iv 2 1 1 2 Range 3 4 Function Domain 4 1 5 KU 1 5 KU

a How do you determine if a relation is a function

Change the percent to a decimal number 5 85 5 85

4 Suppose that f and g are functions with the rules 4 x f x and g x 49x 4 O 7x 7x 16 O 7x 4 O 7x 16 7x Find gof x g f x O 7x 4

18 Which one of the following is equivalent to expressions ex ex 2 O e x O ex 2 x O exi O ex x O ex 2 x

Part a Assume that the height of your cylinder is 6 inches Consider A as a function of r so we can write that as A r 2 2 12 r What is the domain of A r In other words for which values of r is A r defined Part b Continue to assume that the height of your cylinder is 6 inches Write the radius r as a function of A This is the inverse function to A r i e to turn A as a function of r into r as a function of A r A Hints To calculate an inverse function you need to solve for r Here you would start with A 2 r 12 Tr This equation is the same as 2 r 12 r A 0 which is a quadratic equation in the variable r and you can solve that using the quadratic formula You will want to keep A as a variable when you plug the values into the quadratic formula If you want to type in 3 1 in Mobius in text mode you can type in 3 pi 1 x 1 There is x 1 more information in the Introduction to Mobius unit Part c If the surface area is 300 square inches then what is the radius r In other words evaluate r 300 Round your answer to 2 decimal places Hint To compute a numeric square root such as 17 3 you could Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in sqrt 17 3 Use a browser to connect to the Internet and type in sqrt 17 3 into a search field Use a calculator The radius is Number inches if the surface area is 300 square inches

Find the limit and use a graphing device to confirm your result graphically 5 x 125 X 0 lim X40

7nt Several research papers use a sinusoidal graph to model blood pressure Suppose an individual s blood pressure is modeled by the function P t 20 sin 3 where the maximum value of P is the systolic pressure which is the pressure when the heart contracts beats the minimum value is the diastolic pressure and t is time in seconds The heart rate is the number of beats per minute a What is the individual s systolic pressure b What is the individual s diastolic pressure c What is the individual s heart rate a The individual s systolic pressure is Simplify your answer

Prove via calculus by minimizing the sum of square erros that solution of the regression coefficients are b1 sy sx r b0 vbar b1 xbar

A movie complex is showing the same movie in three theaters In theater A 63 of the 70 seats are taken In theater B 52 seats are taken and 28 seats are empty In theater C 24 of the 60 seats are empty Which theater has the greatest percent of its

want the answer for this question using MatLab Code After plotting the following functions over the given intervals please spe whether these functions have roots in the specified intervals or not In addit specify which extreme point the root is closer to 1 f x log x 2x and a b 2 2 2 f x e x 50x and a b 1 3

the Venn diagram to determine the set An B COXS

Select one a a Radiation I Absorption Emission and Transmission Question 3 A quantum is the minimum amount of energy lost or gained by 18 a nucleus in an atom an electron in an atom O O a frequency of light O a wavelength of light

Which of the following graphs represents the equation y 2x 2x 6 O Si Report an Error question 4 of 5 Quiz Next Lesson FOIL face Multiplying B Method Quiz Multiplying Bi Practice Probl How to Factor Quiz Factoring Qua with a Non 1 How to Compl Completing th

What is the equation of the axis of symmetry of the parabola given by the equation y 6 x 1 x 5 Oy 2 Oy 2 O x 2 O x 2 Report an question

BCA oose the correct answer below A U B B CITS OC

5 Decompose i ii X5 2x4 x X 5 x3 2x x 2 into partial fractions show all the steps 4x 14x 2 4x 1

20 6 pts Find a formula for the sinusoidal function whose graph is shown below f x 13

Characteristic Non permissible Values Behaviour Near Non permissible Value End Behaviour Domain Range f x g x 2 I Equation of Horizontal x 0 x 0 y 0 Equation of Vertical x 0 Asymptote y 0 0 3 3 00 0 0 yly 0 x 3 2 x 6x 9 y 0 h x x 3

Exercise 4 The graph below is one complete cycle of the graph of an equation containing a trigonometric function Find an equation to match the graph M 2 5

Write an explicit formula for the sequence 1 3 an 1 1 4 5 1 1 6 7 1 8

4 1 point The table represents a quadratic function What is the missing value y 6 8 0 1 SAWN 4 5 a 22 38 56 b 12 C d 28

3 1 point The quadratic function y x x 1 passes through the point d 1 3 a 1 3 b 1 1 c 1 1

12 1 point Which is not an example of a transformation a vertical stretch b vertical compression c modification d reflection in the x axis

6 1 point Given the graph of y x 3 2 4 what is the vertex a 3 4 b 3 4 c 4 3 d 4 3

1 Solve the following equation inequality for r ER where and z max z Z is the greatest integer floor function z min Z 2r is the least integer ceiling function a 1 2 b 1 9 0 c 2 1 x 1 12 0 d 4 2r 3 4

A meat market combines ground beef and ground pork in a single package for meat loaf The ground beef is 75 lean 75 beef 25 fat and costs the market 2 10 per pound lb The ground pork is 60 lean and costs the market 1 35 lb The meat loaf must be at least 70 lean If the market wants to make at least 180 lb of mea loaf by using at least 50 lb of its available pork but no more than 460 lb of its available ground beef how much ground beef should be mixed with ground pork so that the cost is minimized How many pounds of each kind of meat should be combined to achieve minimum cost pounds of ground pork The meat market should combine pounds of ground beef and Type exact answers Type integers or simplified fractions

4 The height of the water in the Petticodiac river at high tide was measured to be 13 m After 6 H the depth of the water was found to be 1 m a b C Draw a graph of height of the water for a 36 h period starting at high tide Find an equation expressing the depth of the water hours after high tide What height will the water be at 20 h after the initial high tide

Choose the correct answer below OA The statement is true is equal to the empty set OB The statement is false is a set but is not OC The statement is false two sets cannot be equal if they are not equiv OD The statement is true is equivalent to every set

nformation Find and list important information in the problem The table shows the daily attendance for a swimming pool over a period of 2 weeks Daily Attendance 269 282 52 216 239 242 285 54 259 259 The pool manager wants to determine the typical daily attendance Which measure should the manager find and why A The mean because it is influenced by outliers B The median because it is not affected by a few outliers C The interquartile range because it gives the range of the middle 50 of the attendance values D The mean absolute deviation because it gives the average distance of the attendance values from the middle 264 252 1