Complex numbers Questions and Answers

11 5 points Use the graph of f x to sketch the graph of y f x 1 3 f x 31 4 1 1 0 F 2 1

12 5 points Let f x x 3 find and simplify the difference quotient f x h f x h 0 h

7 4 points Circle the letter of any of the following graph s that represent a function a b 54 21 t 24 1 47 3 2 d co 1 I da 3 5 4 3 2 1

Use synthetic division to show that x is a solution of the third degree polyno Enter your answers as a comma separated list x 2 x 4x 2x 8 0

Consider the following function Function f x 6x 35x 8x 12 a Verify the given factors of f x 2x 1 1 1 20 3x 2 w N 6 35 Factors 2x 1 3x 2 6 35 6 32 4 6 39 3 8 26 8 16 12 12 b Find the remaining factor s of f x Enter your answers as a comma separated list c Use your results to write the complete factorization of f x

Factor and simplify cos x cos xsec x Choose the correct simplification below OA cos x OB sin x O C 1 OD tan x sin x

Find all zeros of the function and write the polynomial as a product of linear factors 3 f x x x 25x 25 2 O A f x x 1 x 5 x 5i O B f x x 25 x i x 1 O C f x x 1 x 1 x 25

Write the complex number in polar form Answer exactly in radians with r 0 and 0 0 2 A 1 16 HIG cis

Consider the function f x 11 Graph the exponential function by hand 2 Identify any asymptotes Identify any intercepts 2 250 200 150 100 3 O S 250 200 150 100 50

Find the sum j 3 3

Consider the following Y 2 In 2 In x yz In 4x e Use a graphing utility to graph the two equations in the same viewing window O b Use the table feature of the graphing utility to create a table of values for each equation Round your answers to two decimal places If an answer does not 0 1 2 3 L K S Vy

10 Illustrate the following Use rectangles or circles for the wholes 5 15 18 6

Determine intervals on which the function is increasing decreasing and constant On what intervals is the function increasing OA 4 2 O B 9 4 and 3 8 O C 4 2 and 6 8 O D 3 8 On what interval is the function decreasing On what interval is the function constant 10 W 10 10 e X 10 Time Remaining 01 41 09 G

The formula S 16t is used to approximate the distance S in feet that an object falls freely from rest in t seconds The height of a building is 1005 feet How long would it take for an object to fall from the top The object would fall for seconds Simplify your answer Type an integer or a decimal rounded to the nearest tenth

Evaluate the expression 14 11 3 14 11 3 Simplify your answer Type an integer or a fraction

Name the integers from the list below 1 5 8 33 18 0 75 6 71 14 1 D 1 What are the integers Select all that apply DA 5 33 G 1 1515515551 1 1515515551 B 6 71 E 18 H 75 C 0 0 V 6

Graph the following function Check your result using a graphing calculator f x O A x 2 for x 5 2 for 5 x 6 Choose the correct graph below 8 1 2 forx26 Q OB A THA cal to Ay 2 H ta G O C 20 i tot do 8 HTT 10 g BEL O 20 O D LINY e Ay

Find the inverse of f x x 3 by thinking about the operations of the function and then reversing or undoing them Choose the correct answer below OA f x x 3 OB f x x 3 OC f x y 3 OD f x y 3

The graph shown below approximates the number of children in a country who lived with only their grandparents in the years from 1991 through 2009 The number of children is a Function f of the year x Approximate the number of children living with only grandparents n 1991 That is find f 1991 Number of children in millions 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 91 93 95 97 99 01 03 05 07 09 Year The number of children living with only grandparents in 1991 is appro million Type an integer or a decimal T

Use the graph to find the following a f 2 b the domain c any x values for which f x 1 d the range VITAL I Pit anys UCIC BIG CUITCUL CIVICE UCIOW au cuessary answer box es to complete your choice O A y ly OB y lyz OC yl sys OD ylys O E The range is all real numbers i 4 S 7 This question 1 point s pos 3 4 64 B 10 1 More 10

Suppose a polynomial function of degree 5 with rational coefficients has the given numbers as zeros Find the other zero 4 3 1 4i 3 The other zero is

Determine the other factor for 2ax 4ay 3bx 6by if one of the factors is 2a 3b A B C x 4y x 2y x 2y D x 2y 2

Factor the following quadratic expression 15x 35x A 7x 5x 6 B 5x 3x 7 C 3z 5x 1 Not factorable

Use the graph to find the following a f 2 D the domain c any x values for which f x 1 d the range For what x value s is f x 1 Select the correct choice below and if necessary fill in the answer box to complete your choice A X Use a comma to separate answers as needed OB There is no value of x for which f x 1 What is the range Select the correct choice below and if necessary fill in the answer box es to complete your choice CO 10 k 7 10 8 8 4 2 6 10 O 0 10

Determine whether the correspondence is a function Domain 4 3 6 Range 4 Is the correspondence a function O A Yes because each element in the range corresponds to exactly one element in the domain OB No because an element in the domain corresponds to more than one element in the range C No because an element in the range corresponds to more than one element in the domain OD Yes because each element in the domain corresponds to exactly one element in the range

10 28v 16v 21v 12 12 49x 35x 56x 4

Factor each completely 1 8r 647 r 8 3 12x 2x 30x 5 5 63n 54n 105n 90

The perimeter P in yards of a soccer field is represented by the formula P 21 2w where is the length in yards and w is the width in yards W 10 yd l 100 yd a Solve the formula for W b The perimeter of the soccer field is 330 yards Find the width of the field Width yards c About what percent of the field is inside the circle Round to the nearest tenth of a percent The percent of the field is C

f x 2x 5 Find fog 3 fog 3 g x is as defined in the function below 9 8 7 6 5 3 2 1 9 8 7 6 5 4 3 2 1 N 2 3 45678 5 6 8 y 3 0 2 8

At Generic Middle School 8 students were sick with the flu on the first day of school By the end of the first week 12 students were sick and by the end of the 2nd week there were 18 students sick The attendance clerk noticed that the number of students getting sick was growing exponentially with a growth factor of 1 5 A function model that describes the number that have gotten sick would S x 8 1 5x where x is the number of weeks completed at school Using the model how many students could be expected to have been sick by the en of the 6th week approximately 41 students approximately 205 students O approximately 91 students approximately 72 students

f x x 5 g x is as described in the table below g x A 17 Find fog 9 B 25 C 95 C H 10 2 2 6 3 12 4 20 5 30 6 42 7 56 8 72 9 90 10 11

An airplane is flying with a constant altitude at a speed of 450 mph in a direction 10 north of west directly towards its final destination The airplane then encounters wind blowing at a steady 32 mph in a direction 75 north of east a Start by drawing a vector diagram for this situation Did you draw a diagram Yes Great Your diagram might look something like this i Speed 448 55 ii Direction 0 11 Wind b If the pilot does not correct his course after encountering the wind at what speed and in what direction counterclockwise from east will the plane be traveling 0 1116 mph New Path Original Path Preview Preview c If the airplane had encountered no wind at all it would have reached its final destination in two hours along its original course Assuming the pilot never corrected his course and that the wind continues to blow at the given speed and direction how far from its final destinations is the airplane after two hours of flying under the given conditions miles Preview 0 1116 0 1116 Truagain Look at the diagram in nart a If the wind blows at 32 mph for two hours how many miles will the wind move the plane

5 Find the equation of a line that passes through 5 2 and 1 3 in a point slope form b slope int form c general form

4 What is the value of r given that 10 6 4r a 4 b 1 c 4 d 1 5 What is the value of x given that 20 4x 4 a 4 b 4 c 8 d 6

b How much of the financial goal comes from deposits and how much comes from interest Periodic Deposit Rate at the end of every three 2 5 compounded quarterly months Click the icon to view some finance formulas Time 4 years b of the 25 000 comes from deposits and Use the answer from part a to find these answers Financial Goal 25 000 a The periodic deposit is Do not round until the final answer Then round up to the nearest dollar as needed comes from interest Round to the nearest dollar as needed CHEERD Formulas In the provided formulas P is the deposit made at the end of each compo period r is the annual interest rate of the annuity in decimal form n is the of compounding periods per year and A is the value of the annuity after ty P 1 1 A P 1 r 1 r A P A H 2

1 a cos 60 State exact answer not necessary to show afly a cos 150 co 30 a 0 COS 30 sin 240 Sin Go Sin 60 2 Solve for 0 such that 0 0 360 3 sin 0 2 Sine 60 0 240 and 30 10 sin 0 Sim 45 1 2 2 135 and us b sin 45 a cos 0 090 and 278 d tan 315 tan 45 tan 31s 1 f b tan 330 tan 80 tan 30 53 tan 0 1 b tan ys 8 185 and 315 Sin cos b Ton O COS S 60 pot a 455 A fc 0 135 and 225 6 0 and O 120 tan 0 1 3 tan 30 0 210 and 330 793 128

A fair coin is tossed three times in succession The set of equally likely outcomes is HHH HHT HTH THH HTT THT TTH TTT Find the probability of getting exactly one tail The probability of getting one tail is Type an integer or a simplified fraction

What is the quotient 3x 4x 15 x 3 O 3x 5 3x 5 O 3x 1 3x 1 r 1

Write the equation of the graph shown below in factored form 0 Of x x 2 x 1 x 3 f x x 2 x 1 x 3 f x x 2 x 1 x 3 f x x 2 x 1 x 3 5

eview Quiz What will it cost to carpet a rectangular floor measuring 24 feet by 12 feet if the carpet costs 29 49 per square yard It will cost

Find the intercepts and asymptotes If an answer does not exist enter DNE Enter your asymptotes as a comma separated list of equations if necessary x intercept y intercept 8x 18 x 8x 16 vertical asymptote s horizontal asymptote 10 x y 1 x y Sketch a graph of the rational function y 10 10 y 10 10 10 10 5 y 10 N 10 10 State the domain and range Use a graphing device to confirm your answer Enter your answers using interval notation domain 10

Using division what is the quotient 2x3 2x 12 x 2 O2x 4x 6 O 2x 4x 6 O 2x 4x 6 O2x 4x 6 1 x 2

Use similar triangles to solve A person who is 6 feet tall is standing 90 feet from the base of a tree and the tree casts a 100 foot shadow The person s shadow is 10 feet in length What is the height of the tree The height is yd 90 ft 6 ft 10 ft

Convert the given unit of weight to the unit indicated 620 mg to g 620 mg 9

Let p and q represent the following statements p 6 3 9 q 8x5 80 Determine the truth value for the statement pvq Choose the correct truth value below Opvq is false Opvq is true

1 4 4x 12 4 10 3x 11 Topic 5 Equations with subtraction of the variable term 2 20 5 3x 5 4 4 2x 3 4 8 6x 6 12 4 8x

7 2 2 3 10 12 6x 4 x 8 12 3x 6 11 20 4x8 9 8 2x 4 12 18 x 6 3

7 4 x 8 2 10 4x 12 8 X X 4 10 11 3x 1 13 9 5 x 10 3 12 6x 10 2

Can you identify each function and type the correct code Please remember to type in ALL CAPS with no spaces Puzzle 1 1 Identify the function 3 Identify the function Your answer 2 Identify the function 4 Identify the function IZ Keep trying You can do it answer choices A B C Y X 1 2 4 Y X 1 4 Y X 4 3 D F Y X 4 2 3 Y X 2 2 4 Y X 3 4 E G I H Y X 1 2 4 Y X 3 4 Y X 2 4 Type the 4 letter code into the answer box All CAPS no spaces 20200 02020 Scaficided Mail and Science

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