Functions Questions and Answers

The function is graphed below State the values that fulfil the If there are no such values type DNE If there are multiple discrete values separate them with commas If there are a whole Interval of values that fulfill the requirement use Interval notation to give all of the values in the Interval Type oo for co and oo for oo Also type U for U y 1 5 2 2 1 5 0 7 0 2 0 5 1 2 1 1 5 1 0 5 0 0 5 Where is f at 1 1 0 1 5 1 24 Where is f 0 Vz in the Interval 0 7 0 2 Where is 0 Vz in the Interval 0 5 What are the values in the closed interval 1 2 1 5 where f undefined at z What are the critical values of f at z 1 1 5 Image developed from imago at Svesen KH Where does have local minimums What are these local minimum values the relative minimum is occurs at x Where does have local maximums the relative maximums occur at z which Where does have absolute minimums What are these absolute minimum values the absolute minimum is occurs at I occurs of I which Where does have absolute maximums What are these absolute maximums values the absolute maximum is which

Problem ID PRABMQ2W Evaluate the expression 6 2019 illustrative Mathematics All Rights Reserved Type your answer below as a number example 5 3 1 4 1 2 or 3 2 Submit Answer

Problem ID PRABMQ2B Write a polynomial function p x with degree 3 that has p 7 0

Problem ID PRABMQ2A Select all the polynomials that have x 4 as a factor A x 13x 12 B x 8x 19x 12 C x 6x 5x 12 x 10x 8 D x E x 4 2019 Illustrative Mathematics All Rights Reserved Select all that apply OA OB Oc OD

FTUDICHIV Find the value of each variable that makes the equation true 25 2 29 74 7 77 1 64 Fill in the blank 8c 7 2 a 2019 Illustrative Mathematics All Rights Reserved Type your answer below as a number example 5 3 1 4 1 2 or 3 2 8 Correct Submit Answer Next Problem Problem ID PRABMQ2R Fill in the blank

43 Sixd f x sina g x cosa c then X 8 sin x 8 an be 2 f x 2x dx Ax8 Carctanx k dx A x 4 A 2 CD 1 4 C D 0 2 x 3 Btan x 6 C 2 B 12 4 B 1 6 RU 0 R satisfy the f x 2xf y y and x e x cos4x dx then 54 41 5 2 2 3 x tan 1 1 4 9 x tan x 3 x c SECTION C Linked Comprehension Type Question paragraph some multiple choice questions a This section contains 4 paragraphs Based up answered Each question has 4 choices 1 2 4 out of which ONLY ONE is correct Comprehension l Reduction formulas can be used to compute higher power of sinx cosx tanx etc Choose the correct answer 1 sin4 x cos x Asin 5 cos x c then A equals sin x dx 1 3 2 15 4 15 2 tan xdx 1 3 1 A 3 x c 3 A 2 3 1 A 1 3 2 4 tan5 x Atan x X Y D 4 A 3 sec xdx tan x Atan xe ta xdx 5 2 A X COS 2 A Choos If 1 1 3 3 If 1 3 Compre m 1 n ax b Integer function in

A produce buyer for a juice company is buying peaches He makes a choice of either Oregon Michigan or imported peaches For this contract he must also choose fancy or extra fancy Wi the sample space and assume each outcome is equally likely Then give the probability of the requested outcomes in parts a and b below CEITES Write out the sample space Choose the correct answer below OA S Michigan fancy Oregon fancy Oregon extra fancy imported extra fancy OB S Michigan fancy Michigan extra fancy Oregon fancy Oregon extra fancy Washington fancy Washington extra fancy imported fancy imported extra fancy C S Michigan fancy Michigan extra fancy Oregon fancy Oregon extra fancy imported fancy imported extra fancy OD S Michigan fancy Oregon extra fancy imported extra fancy a The peaches selected are fancy Type an integer or a simplified fraction b The peaches selected are from Oregon or fancy

A man wants to adopt a puppy from an animal shelter At the shelter he finds eight puppies that he likes a male and female puppy from each of the four breeds of beagle borzoi dalmation and pekingese The puppies are each so cute that he cannot make up his mind so he decides to pick the dog randomly Find the probability that the man chooses anything but a pekingese

9 What do the x intercepts of the graph represent in the context of the problem situation 10 How does increasing the c value from 0 to 6 translate the graph Why 11 How does increasing the c value from 0 to 7 translate the graph Why 12 What happens to the parabola when the c value is increased c 0 13 What happens to the parabola when the c value becomes negative c 0 14 How is the graph of y x 1 similar to the graph of y x 1 How are the graphs different

4 Sketch a graph of y x What is the name used to describe a graph with this shape What type of function rule creates a graph with this shape

2 Sketch graphs of each of the following functions and complete the indicated information about function a y 4x b y 1 x Coordinates of vertex Axis of symmetry Coordinates of vertex Axis of symmetry

graph y x compare to the graph of y about the domain and range of the mathematical function y x 4 2 2 y 1 00x2 4 2 y 12 ix does

11 Sketch the graph of y 2x What are the coordinates of the vertex of the graph and what does this indicate about any maximum or minimum values of the function

15 Sketch a graph of y x 2 What are the coordinates of the vertex

3 Sketch a graph of y 3x 2

13 The sum of the binomial coefficients of 2r equal to 256 The constant term in the expansion is a 1120 b 2110 c 1210 d None of these 14 The sum of the co efficients in the expansion of 1 2x 5x y is d and the sum of the co efficients in the expansion of 1 x 2 is b Then a a b c a b b a b d ab 1 3n 15 The binomial expansion of 1 N ne 18 contains a term independent of x a only ifk is an integer

Analyze the data in this table to determine whether they can be modeled with a quadratic function Jos s Soccer Kick Time sec Height m First differences Second differences 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 A 0 0 2 0 4 0 6 0 8 1 0 1 2 1 4 1 6 1 8 2 0 0 1 76 3 14 4 12 4 7 4 9 4 7 4 12 3 14 1 76 0 1 76 1 38 0 98 0 58 0 2 0 2 0 58 0 98 1 38 1 76 0 38 0 4 0 4 0 38 0 4 0 38 0 4 0 4 0 38 2 How does the graph of y x h compare to the graph of y x when h is positive 3 How does the graph of y x h compare to the graph of y x when h is negative 4 How does the graph of y x h compare to the graph of y x

5 Describe the transformations on the graph of the parent quadratic function needed to find a function that represents the height of a soccer ball as a function of time as illustrated by the dotted graph y 24 18 626 12 12 9 6 3 61 12 18 3 6 9 12 x 1

15 Consider the functi a Sketch a graph of the function b Answer these questions based on the graph What are the coordinates of the vertex of the parabola Does the function have a maximum or minimum value What is that value

11 Consider the given graph How does this graph compare to the graph of the parent quadratic function y x 12 What function is represented by the graph 6 5 4 3 2 1 y 0 11 10 8 6 42 1

0 Height of ball y 5 4 3 2 tex of the parabola Vertex 1 4 9 Time 4 5 x

For what polygon is the sum of its interior angles 1800 A 20 gon B Dodecagon C Decagon A B C D D Octagon E Hexagon

12 This graph and equation each show the distances y in kilometers of two different cars from a destination after x hours 1 14 240 180 60 90x 180 90 0 180 0 180 180 Distance from Destination in kilometers 240 160 80 Car A 012345 Time in hours What is the difference between the cars initial distance in kilometers from their destination A 10 kilometers B 60 kilometers C 170 kilometers Car B y 90 180 D 180 kilometers

Write the constraint below as a linear inequality A canoe requires 6 hours of fabrication and a rowboat 7 hours The fabrication department has at most 107 hours of labor available each week Let x be the number of canoes and let y be the number of rowboats Choose the inequality that represents the given constraint OA 6x 7y2 107 OB 7x 6y 107 Submit quiz OC 6x 7y 107 D 7x 6y2 107

Which set of angles are complementary in this diagram D E LECF and ZBCF O ZECF and ZDCE ZDCF and ZBCF ZECF and ZACF B F

Decide whether the sequence can be represented perfectly by a linear or a quadratic model 7 16 31 52 79 112 This sequence can be represented perfectly by a quadratic Therefore we can generate the following system of equations a b c 4a 2b c 9a 3b c Solving this system we have the following a b C model

Solve the system of two equations in two variables 9x 103 8y 3x 2y 11 OA 8 6 OB 7 6 OC 7 5

Perform the indicated operation where possible 3 OA O B OC 2 3 2 4 5 5 1 3 5 8

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent dependent or inconsistent x y z 8 5x y z 0 x y z 20 O A Independent OB Inconsistent Dependent

given and the equation pass The cost in dollars of manufacturing items is given 2 by C x x 7x 15x what is the corst of manifacturing 6 items manifachting 310

State the domain of the function FCX 7X 5

6 3x 100 x where x is a number of percent and y is the cost in thousands of dollars of removing x percent of a given pollutant Complete parts a through c y a Find the cost of removing each percent of pollutants 50 70 80 90 95 98 99 50 70 80 90 95 98 99 Type an integer or decimal rounded to two decimal places as needed b Is it possible according to this function to remove all the pollutant y O No OYes c Graph the function Choose the correct graph below OA O B Q Q O C O D

16 answer the questions that follow a Use the Leading Coefficient Test to determine the graph s end behavior OA The graph of f x rises left and rises right OB The graph of f x rises left and falls right OC The graph of f x falls left and falls right OD The graph of f x falls left and rises right b Find the x intercepts X Use a comma to separate answers as needed At which zeros does the graph of the function cross the x axis Select the correct choice below and if necessary fill in the answer box to complete your choice OA X Use a comma to separate answers as needed OB There is no solution At which zeros does the graph of the function touch the x axis and turn around Select the correct choice below and if necessary fill in the answer box to complete your Use a comma to separate answers as needed OA X

Q2 Prove xn 1 for n 3 Pax 1 d n d n

Given u u v with u ex 3x y and v e y x 4y and the circle C with radius r 1 and center at the origin 3 Evaluate the integral of u dr u dx v dy on the circle from the point A 1 0 to the point B 0 1

A dress regularly sells for 142 The sale price is 104 Find the percent decrease of the sale price from the regula price Round to the nearest tenth of a percent A 36 5 B 73 2 OC 273 7 OD 26 8

Select one A sequence is defined recursively by the following rules f 1 3 f 2 7 f n 1 f n f n 1 Which of the following statements is true about the sequence O f 3 11 a a a Of 6 43 O f 5 25 O f 4 17

Lillian Fok is president of Lakefront Manufacturing a producer of bicycle tires Fok makes 1 200 tires per day with the following resources 400 hours per day 12 00 per hour 21 000 pounds per day 1 00 per pound 5 000 per day 10 000 per day a Labor productivity per labor hour for these tires Labor Raw Material Energy Capital tires labor hour round your response to two decimal places

81 Select one Linear Quadratic Exponential Review Question 7 Find the equation of the linear function that passes through the point 1 4 and has a slope of 6 61 y 6x 10 O y 6x 2 Oy x 4 Oy 6x 25

Select one Linear Quadratic Exponential Review Question 1 Which equation represents the line with a slope of and passing through the point 4 7 01 O 81 60 5x 3y 1 O 3x 5y 23 O 3x 5y 47 O 5x 3y 41

Use only sin 30 0 30 0 0 0 and sin 30 30 0 30 27 8 17 Use Linear approximation to estimate sin 30 13 What is the error

Which of the following transformations are linear 0 A B PE 91 7 C Y2 9 Y3 3 D 91 8x16x2 2x3 y2 5x27x3 Y3 3x19x2 F y x Y2 X3 Y3 21 y x 5 Y2 X2 3 7x1 x2 Y2 X1 91 0 92 9x b

in the graph to the right The function has a maximum of at x The function has a minimum of at x The function is increasing on the interval s The function is decreasing on the interval s The domain of the function is The range of the function is 10 10 9 8 7 6 7 8 19

Solve equation by using the quadratic formula 4t t 9 0 Simplify answers List multiple answers with a comma in betweer

Solve the initial value problem 8y 2y y 0 subject to y 0 0 2 y 0 0 325

What is the area of a transducer whose diameter is 4 5 8 inches 61 8 square inches 67 20 square inches 16 8 square inches 14 53 square inches

A gear with 54 teeth is meshed to one with 18 teeth Write the relationship as a ratio reduced to lowest terms 6 2 9 2 9 1 3 1

How much sheet metal does it take to construct a box that is 2 x 3 x 6 72 sq ft Both 72 sq ft and 10 368 sq in are correct 75 sq ft 10 368 sq in

a is a rational function given in both standard and factored forms et f x 52 8 x 1 4x 3 nd 52 8 4x x 3 the domain in interval notation ote Use oo for 00 oo for co U for union the y intercept at the point x intercepts at the point s Vertical asymptotes at x Horizontal asymptote at y

The graph of the function f x 6 3 can be obtained from the graph of g x 6 by one of the following actions a shifting the graph of g x to the right 3 units b shifting the graph of g x to the left 3 units c shifting the graph of g x upward 3 units d shifting the graph of g x downward 3 units e reflecting the graph of g x in the x axis f reflecting the graph of g x in the y axis Your answer is input a b c d e or f Is the domain of the function f x still Your answer is input Yes or No The range of the function f x is A the value of Ain