Complex numbers Questions and Answers

Give the rule of the function shown below which is a vertical shift of a basic logarithmic function 2 1 2 3 4 5 Y 2 6 Shift Scroll to zoom Shift Drag to pan t er 30 6 X 8

Let g x 2 The following graph shows g x for a between Y a Find g 9 b Find g a 2 5 N 1 5 0 5 1 3 1 2 1 1 9 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 X

Identify the missing number without using a calculator If no number makes the statement true enter DNE a In 1 e b logo 36 c log3 81 d log 1 e logg 9

Consider the logarithmic expression below and answer the following loga 64 What is this expression equivalent to O The result of 4 divided by 64 O The exponent needed on the base 4 to produce the result 64 O The fourth root of 64 The result of 64 divided by 4 Evaluate the logarithm Explain O 16 because 4 64 1 6 O 16 because 64 4 16 O3 because 4 64 O 2 2 because 64 2 2

Khan Academy What is the range of f A 7 6 5 4 3 2 Choose 1 answer Y 7 6 5 4 3 2 1 2 do 3 40 7 5 6 7 1 2 3 4 5 6 7 The f x values 6 0 2 4 and 7 4 f x 5 6 f x 7 The f x values 4 3 1 and 5 C

um revenue B Complete the following tables for Celsius and Fahrenheit c What can you conclude about the relationship between Fahrenheit and Celsius 32 You travel often therefore you need to be able to convert Celsius to Fahrenheit so you know what types of clothes to pack for each trip A Given the following equation that represents Celsius in terms of Fahrenheit find the equation for Fahrenheit in terms Celsius C F 32 F 50 68 8 86 Price doll 16 12 0 10 20 24 30

A tb C 1 am

If UV 2x VW x 1 and UW 7 what is UV

You go to We Love Math Ice Cream Shop where they identify their cone selections by volume The sign in the store states that the volume V of their circular cones are V h It also states that all of the cone heights are 4 times the radius A Express the volume V as a function r B Evaluate the volume of the large cone with a diameter of 3 inches

27 Suppose that the revenue R in dollars from selling x cell phones in hundreds is R x 1 2x 220x The cost C in dollars of selling x cell phones is C x 0 05x 2x 65x 500 a Find the profit function P x R x C x b Find the profit if x 15 hundred cell phones are sold

28 The volume of a cylinder varies jointly as radius squared and height a If the constant of variation is n create an equation to represent this relationship b If the radius is 4 2 and the height is 12 5 find the volume of the cylinder

31 Simplify 5a4b 2a b 32 Simplify 5 18 6 50

14 Given f x and g x x find the following expressions x 5 a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 Type an exact answer using radicals as needed Simplify your answer

Evaluate each expression using the graphs of y f x and y g x shown below a gof 1 b gof 0 c fog 1 d fog 4 a gof 1 4 Simplify your answer b gof 0 Simplify your answer C 8 yg x 6 4 y f x

State whether the following statement is true or false If f x x and g x x 9 then fo g 2 3 Choose the correct answer below O A True because g 2 2 9 and f 2 9 3 OB True because f 2 2 and g 2 3 OC False because f 2 2 and g 2 3 OD False because g 2 2 9 and f 2 9 3

Exam An airplane flew from a town A to a town B 50km away on a bearing of 210 It then flew from town B to another town C on a bearing of 150 If town C is 80km away from town B find a i b ii the distance between A and C correct to the nearest kilometer the bearing of A from C to the nearest degree How far East of B is C

OA a 26 7 b 44 5 c 30 d 45 This question 1 point s possible For the given data set find the a mean b median c mode or state that there is no mode and d midrange The ages of teachers in the mathematics department of a certain high school are shown below 30 55 33 60 30 55 30 46 46 43 OB a 42 8 b 44 5 c 30 d 45 OC a 31 3 b 44 5 c 30 d 45 Some acco available u OD a 42 8 b 44 5 c 46 d 45

A graphing calculator is recommended A company s marginal cost function is MC x 28e x 5 dollars where x is the number of units Find the total cost in dollars the first hundred units units x 0 to x 100 Round your answer to the nearest cent 7313 05 x

Solve 1 1 cos x sin 2x The smallest positive solution is The next smallest positive solution is

Suppose that the monthly cost in dollars of producing x chairs is C x 0 006x 0 07x 19x 700 and currently 70 chairs are produced monthly a What is the current monthly cost b What is the marginal cost when x 70 c Use the result from part b to estimate the monthly cost of increasing production to 72 chairs per month d What would be the actual additional monthly cost of increasing production to 72 chairs monthly

3 The marked price on a box of chocolates is 15 If the after tax price is 16 20 what percent is the sales tax I

5 7 REVIEW SUM 2 Q2 Solve each system by elimination 5 4 8x 4y 8x 6y 2 A 1 8 C 1 1 A Sketch the solution to each system of inequalities 7 y21 8 B C B 1 1 D 8 1 D 6 6 9 x 13 y x 0 A 3 10 C 10 3 8 x y 1 x 2y 4 A B 6 D B 3 10 D 3 10 K

A 3 Each point on the graph represents a polar bear Explain the answer to each question below Heights and Masses of 8 Polar Bears E 4 2 Height m 14 0 a Which bear has the greatest mass What is this mass b Which bear is the shortest What is its height c Which two bears have the same mass What is this mass 10 d Which two bears have the same height What is this height 8 A B 4 This graph shows the height of the tide in a harbour as a function of time in one day Explain the answer to each question below Height of the Tide in a Harbour 6 B 4 0 00 00 H 200 400 600 800 Mass kg 06 00 12 00 18 00 24 00 Time 24 h clock a What is the greatest height At what times does it occur b What is the least height At what times does it occur c How high is the tide at 04 00 d When is the tide 4 m high 5 To raise a flag Sepideh pulls the rope steadily with both hands for a short time then moves both hands up the rope and pulls again She does this until the flag has been raised Which graph best represents the height of the flag Give reasons for your choice Graph A Graph B Time s Graph C Distance from home km Time s 2 0 6 Gill runs for exercise This graph shows her distance from home during one of her runs Describe Gill s run for each segment of the graph Gill s Run 1 0 O A B Time s Graph D D 20 30 10 Time min Time s 5 3 Interpreting and Sketching Graphs 281

6 x 6y 42 7x 3y 24 A B D 8 8 14 8 4 V V x X X X

Graph linear Inequalities Sketch the solution to each system of inequalities 2 1 y x 3 y 3x 1 A B 6 D y V y X X X

11 11 y x 3 x 3 4 3 2 1

3 x 3y 9 x 3y 3 A B O D T 2 A R N y y y V A2 y X x X

Find a the mean b the deviation from the mean for each data item and c the sum of the deviations in part b for the following group of data items 56 66 61 56 71 a The mean is Simplify your answer

Use the display of data to find the mean median mode and midrange The mean of the data is Frequency 10 8 420 2 Score 10 20 30 40 50 Round to the nearest tenth as needed

Click the icon to view the bar graph Choose the correct answer below OA The bars are not scaled proportionately in terms of the data they represent OB The wrong impression has been created about how the data are changing because equally spaced intervals are not used on the horizontal axis OC The scale of the vertical axis makes the differences in bar height look larger than they really are OD The images in front of or behind each bar make it look as though the bars are taller than they really are Sports Riches Weekly Pay Thousands of Dollars 275 250 225 200 175 150 125 A 100 0 of data F C Barcelona Spain Soccer Oklahoma City Thunder U S A Average Weekly Pay on Selected Sports Teams Toronto Raptors Canada Miami Heat USA Manchester United U K San Francisco Giants U S A New York Yankees U S A S

a Find the domain Use interval notation E b Find the range Use interval notation y E x c Find the y intercept Enter your answer as an ordered pair O Decreasing 100 d Is f x an increasing growing or decreasing decaying function O Increasing equation e Find the equation of the horizontal asymptote Enter your answer as an equatic f Graph the function by dragging the y intercept to the correct position and the

a Graph the function by dragging each of the following to the correct position the horizontal asymptote the y intercept a second point 20 10 10 0 1 10 2 2 10 1

2 Find the equation of a power function passing through 2 2 and 1 8

Determine whether or not the graph shown is the graph of a polynomial function 10 8 6 8 6 16 40 3 5 O not a polynomial funct O polynomial function

Rewrite the quadratic function in standard form f x 2x 6x f x Give the vertex x y

Simplify each of the following Enter the exact answers Enclose numerators and denominators in parentheses For example a b 1 a 729

4 10 points Use the Remainder Theorem and Synthetic Division to evaluate P c for P x 2x 21x 9x 200 at c 9 antanirions sie

Find the domain of the function Enter your answers as a comma separated list X 3 9 The domain of f x is all real numbers except x Find the vertical asymptotes and horizontal asymptotes of the function Enter your answers as comma separated lists of equation vertical asymptote s horizontal asymptote s

24 109 4 3x 2

The graph to the right uses cylinders to represent barrels of oil consumed by two countries Does the graph distort the data or does it depict the data fairly Why or why not If the graph distorts the data construct a graph that depicts the data fairly Does the graph distort the data Why or why not 19 2 Daily Oil Consumption Millions of barrels 5 7 Country A Country B O A Yes because the graph incorrectly uses objects of volume to represent the data OB Yes because 3D objects always distort the data in graphs OC No because the proportions are accurate OD No because the graph is technically correct A

For the functions f x x 3 and g x 5x find the following a fog x and its domain b gof x and its domain a fog x 5x 3 Simplify your answer 3 The domain is Type your answer in interval notation b gof x Simplify your answer 8

In chemistry pH is a scale used to specify how acidic or basic a water based solution is Acidic solutions have a lower pH while basic solutions have a higher pH At room temperature 77 F pure water is neither acidic nor basic and has a pH of 7 A room temperature solution with a pH greater than 7 is basic while a room temperature solution with pH less than 7 is acidic The pH of a solution is given by mol L Hint log where H is the concentration of hydrogen ions in the solution measured in moles per liter mol L Use this formula to address the following items The pH of beer is 4 What is the hydrogen ion concentration of beer ph mol L H The pH of bread is 5 5 What is the hydrogen ion concentration of bread H log log H One can use the propties of logarithms to prove why

The compound interest formula is given by A P 1 5 where A is the accumulated amount after an initial investment of P dollars is invested for t years at annual interest rate r compounded in times per year Use the formula above to determine how long it will take an initial investment of 26 000 to quadruple if the account earns 6 interest per year compounded monthly Round the solution to two decimal places The account balance will quadruple after Use the formula above to determine how long it will take an initial investment of 26 000 to quadruple if the account earns 12 interest per year compounded monthly Round the solution to two decimal places The account balance will quadruple after years years

For the given equation and graph of the quadratic function do each of the following Complete parts a through e f x 2 x 8 2 a Give the domain and range The domain is 00 00 Type your answer in interval notation The range is 0 2 Type your answer in interval notation b Give the coordinates of the vertex The vertex is 8 2 Type an ordered pair c Give the equation of the axis of symmetry The axis of symmetry is x 8 d Find the y intercept s The y intercept s is are Type an ordered pair Use a comma to separate answers as needed AY 40 B

Find the Maclaurin series for the given function 7 cos x What is the Maclaurin series of 7 cos x k 0 Type an expression using k and x as the variables

Explain how you function could restrict the domain of f x 2 x 4 2 5 so that it is a one to one

Use the logarithm change of base formula to convert each of the following logarithms to the specified base Convert log 4 3 from base 14 to base 7 log 4 3w Convert log 3 5p6 from base 13 to base 10 log 5p 6 Convert log 2 92 from base 4 to base e Joga 2 92

x 7x 14 4 Move all terms to the left side of the inequality and then define the left side of the inequality as f x Then list the open intervals determined by the real zeros of f Complete the fol ble ype your answers in interval notation Use integers or fractions for any numbers in the expressions Use ascending order Interval the inequality true or false for a test value on the interval False True

Solve the quadratic inequality Give the solution set in interval notation x x 6 0 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is the single point Type an integer or a simplified fraction OB The solution set is the interval Type your answer in interval notation Use integers or fractions for any numbers in the expression OC The solution set is

Use the properties of logarithms to expand the following logarithmic expression as much as possible Where possible evaluate logarithmic expressions log 10 9 log14 10 9