Algebra Questions

12 Factor the polynomial function f x x 2x 6x 4x 16

4 Explain the difference between 5 2 and 52

5 Divide x4 3x 55 x 3

9 One of the zeros of the polynomial function is 5 What is the factored form of the function f x x 4x 6x 4x 5 o x 5 x 5 x 1 x 1 o x 5 x 1 x 1 o x 5 x 1 x 1 x 1 x 1 x 5

10 What are the zeros of the polynomial f x x x 16x 4x 48

4 Use synthetic division to divide 4x 6x 23x 10 by x 2

1 The table shows ordered pairs for a polynomial function f What is the degree of f 77 7 2 3 f x 82 17 2 17 82

many miles they run each week The following is the data collected from the team this past week 10 15 33 47 52 35 8 72 42 29 45 54 41 37 48 56 45 40 This data is also summarized in the box and whisker plot below T 10 e Weekly Running Distances miles 6 20 30 40 50 60 State whether each of the runners described in the table below would be considered an outlier by se lecting Yes or No 70 Press the hotspot that corresponds to the correct response Press the answer box after each selection to

For the function f use composition of functions to show that 5 7 1 x 7x 1 x 3x 7x 1 is as given 7 To show that f x x find f of x and 1 of x and check to see that each is x only f o f x is is x each is x at least one is x

3 2 1 0 1 2 3 f x 82 17 2 I 2 17 82 2 Which graph represents f x x Explain how you know based on the sign of the leading coefficient and degree of function

Determine whether the function is one to one If it is find a formula for its inverse f x 4x 9 Is the function one to one No Yes Find a formula for the inverse if it exists Select the correct choice below and fill in any answer boxes within your choice A x 0 Simplify your answer OB There is no inverse function

Find the inverse of f x 2x by thinking about the operations of the function and then reversing them Choose the correct answer below X OA f x OB f 1 x O c f x 1 2 x 2x OD f x 1 1 2

Determine whether the function is one to one If it is find a formula for its inverse 3 f x x 5 Is the function one to one O No Yes Select the correct choice below and fill in any answer boxes within your 1 The inverse function is f x B There is no inverse function A choice

For the following function a determine whether it is one to one b if it is one to one find its inverse function f x x 6 Is the given function a one to one function Select the correct choice below and if necessary fill in the answer box to complete your choice O A Yes the function is one to one The inverse function is f x Simplify your answer B No the the function is not one to one

Which equation reveals the minimum or maximum value of f 2 without changing the form of the equation f x x 3 x 4 B f x r 8r 15 f x x 2 1 f 1 2x 1

Daniel claims that if a graph of a quadratic function has zeros at 4 0 and 2 0 then the factored form of the quadratic function could be written as f x x 4 x 2 Is Daniel correct A Yes Daniel correctly wrote out a factored form of a quadratic function with zeros at 4 0 and 2 0 B No Daniel should have written the factored form as f x x 4 x 2 C No Daniel should have written the factored form as f x x 4 x 2 D No Daniel should have written the factored form as f x x 4 x 2

Let f x x 2 Graph a function g which represents a horizontal translation to the right 3 and a vertical stretch by a factor of 2 of the function f Ray Tool Directions 1 Be sure the Ray Tool is on it should be dark grey 2 Click once on the coordinate plane to place the endpoint of the ray 3 Click once on another point to create a ray that goes through your new point 4 Repeat to make another ray as necessary 5 Use the Undo Redo and Reset buttons as necessary to make changes RAY 10 9 A EDIT LABEL

11 How many complex zeros does the function have Explain f x x 3x 5x 3x 6 12 Factor the polynomial function f x x 2x 6x 4x 16

4 The amount of money Veronica has in her savings account after a months is shown in the scatterplot below Savings 3000 2500 2000 1500 1000 500 A 0 B 50 1 2450 2 2150 c 200 3 2100 4 1700 5 1600 6 1450 0 2 4 7 1300 6 Months 8 1000 9 750 8 10 600 10 12 Based on the trend shown in the scatterplot which of the following best represents the amount of money Veronica will have in her savings account at the end of 12 mon A DO

3 Which graph represents f x 2x Explain how you know based on the sign of the leading coefficient and degree of function 4 Use synthetic division to divide 4x 6x 23x 10 by x 2 5 Divide x4 3x 55 x 3

8 What are the factors of the polynomial function Use the rational root theorem factors f x x x 10x 8 The possible rational roots are 1 12 14 18 x 1 o x 1 x 2 x 2 x 4 o x 4 o x 5 O O 9 One of the zeros of the polynomial function is 5 What is the factored form of the function f x x 4x 6x 4x 5 o x 5 x 5 x 1 x 1 o x 5 x 1 x 1 o x 5 x 1 x 1 o x 1 x 1 x 5 10 What are the zeros of the polynomial f x x x 16x 4x 48

Werts a function g whose graph represents a translation 2 units down and 3 units to the right of the graph of f gla

The table below shows the amount of water that is in a fish tank being filled Minutes Gallons of Water 1 A f x 5x 12 B f x 5x 7 f x 7x 5 D f x 12x 5 12 2 17 3 22 4 27 Which of the following functions could model the amount of gallons of water f x that the fish tank will contain after a minutes of being filled

What are the domain restrictions of Oq 1 and q 8 O q 1 and q 8 Oq 1 and q 4 O q 1 and q 4 q 7q 8 q 3q 4

and supply CHIMEDELE System by Elimination Solve each system by elimination O 401 39 0 10y 19 3y 0 A 3 1 C 6 1 x 28 2 018 V Bi 3 1 Dj No solution 8 01 8 EZ 777 A 1 2 1 1 8 CH 10 2 D Infinite number of solutions 48 52 01 E r 1 137 1 V 291 Z Z 8 D 4 2

Simplify 2x 2 x 2x 1 O 2 O 1 x 1 O 2 x 1 2 2 1 1

Which expression is equal to O O O O x 4 x 2 x 2 x 4 x 2 x 4 x 2 x 4 x 2 x 4 x 4 x 4

Which expression is equal to O O O 75 7m 7m5 n4 n5 7m5 4mn8 28m5n 7

What are the domain restrictions of the expression Select each correct answer Oy 8 O y 5 O y 4 0 y 5 Oy 8 Oy 4 y 3y 40 y 9y 20

3 Ethan is writing a customer satisfaction survey for the Brew for You Coffee House he works at He has come up with two versions of the same question Which question creates bias Question 1 How much did you enjoy the cup of coffee you had today Question 2 How would you rate the cup of coffee you had today A Question 1 because it s biased towards a positive answer B Question 2 is biased because the customer has to use a scale to rate the cup of coffee C Neither versions of the question create bias D Both versions of the question create bias

2 A peer reviewed medical journal publishes a report on the results of a clinical trial for a new drug It reports that the clinical trial had 4 012 participants who were given either the drug or a placebo The data showed that there was no statistical significance in the difference between the effects of the drug and of the placebo What statement would be true about the journal s report A The results of the trial may still be valid even though there was no statistical significance B The journal s report is not valid because no conclusions were made regarding the results of the clinical trial C The journal s report is not valid because the clinical trials methodology must have been flawed which is why there was no statistical significance D The journal s report is not valid because no statistical significance indicates that the results of the clinical trial were not medically important

Which is the inverse of f x log 216 C 6216 A B 216 6 216 D X 216 x

4 Is the survey question below biased Explain your reasoning Do you like animals and would you ever consider owning a dog cat or hamster A Biased because it only lists 3 types of animals B Not biased because people can answer without being swayed one way or and C Biased because two questions are being asked at once D Not biased because people can answer yes or no

L A health food store was introducing a new smoothie mix and set up a display offering free samples to shoppers The display was up from 10am to noon on Tuesday and 18 shoppers tried the new smoothie mix Out of the 18 shoppers 7 said they liked the new smoothie mix 8 said they did not like it and the rest were undecided The health food store manager thought the survey was biased but the store worker giving the samples did not think it was biased Who is right about the survey A It is not biased because people gave their honest opinions B It is not biased because the people who tried the product chose to participate in the survey C It is biased because only 17 people tried the product D It is biased because some of the people were undecided about liking the product

8 A student is determining if two functions are inverses of one another The student completes the following computation and concludes that yes the functions are inverses Is the student correct f x 3x 5 g x 5 f g x 3 35 5 x g f x 3x 5 5 3 x A The student is correct because f x is found by adding 5 and multiplying by 3 B The student is correct because the function composition f g x x and the function composition g f x x C The student is incorrect because the functions are not opposites of each other D The student is incorrect because the function composition f g x x and the function composition g f x x proves nothing

5 Matthew claims that the function g x x 2 5 is the inverse of the function of f x 2x 5 Which statement provides a correct analysis of Matthew s claim A Matthew s claim is correct because if you add 5 to g x and then multiply it by 2 you get f x B Matthew s claim is correct because when g x is substituted into every occurrence of x in f x f g x x and when f x is substituted into every occurrence of x in g x g f x x C Matthew s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x 5 therefore g x is not the inverse of f x D Matthew s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x therefore g x is not the inverse of f x

6 Which is the inverse function of f x x 9 A B f x x 9 f x x 12 c f x D f x x 9 x 1

1 3 ut a ftware System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 3 1 3 y 1 x 4 x 28 2y A 8 10 C 8 10 5 x 15 9 y A 7 10 C 4 10 2 2 044 8x 36y 7 8x 4y 4 9 12y 3x A 8 1 C 1 1 B 3 1 D No solution 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 All rights reserved 2 2 x 5 4 4 4 9 x y 5 5 6 8 9 y 0 44 0 2x 8y 4 1 y x 0 2 10 A 1 2 B 1 1 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x 18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

1 3 ut a ftware System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 3 1 3 y 1 x 4 x 28 2y A 8 10 C 8 10 5 x 15 9 y A 7 10 C 4 10 2 2 044 8x 36y 7 8x 4y 4 9 12y 3x A 8 1 C 1 1 B 3 1 D No solution 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 All rights reserved 2 2 x 5 4 4 4 9 x y 5 5 6 8 9 y 0 44 0 2x 8y 4 1 y x 0 2 10 A 1 2 B 1 1 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

1 7 ut a System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 1 3 3 3 1 4 x 28 2y A 8 10 C 8 10 5 x A 7 10 C 4 10 15 9 2 2 0 44 8x 36y 7 8x 4y 4 9 12y 3x ftware LLC All rights reserved A 8 1 C 1 1 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 3 1 D No solution B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 2 6 8 5 4 4 4 9 x y 5 5 A 1 2 B 1 1 10 9 y 0 2 x 44 0 2x 8y 4 1 1 y x 0 2 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

1 3 ut a ftware System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 3 1 3 v 1 x 4 x 28 2y A 8 10 C 8 10 5 x 15 9 y A 7 10 C 4 10 2 2 044 8x 36y 7 8x 4y 4 9 12y 3x A 8 1 C 1 1 B 3 1 D No solution 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 All rights reserved 2 2 x 5 4 4 4 9 x y 5 5 6 8 9 y 0 44 0 2x 8y 4 1 1 y x 0 2 10 A 1 2 B 1 1 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y7x 18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

1 3 ut a ftware System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 3 1 3 y 1 x 4 x 28 2y A 8 10 C 8 10 5 x 15 9 y A 7 10 C 4 10 2 2 044 8x 36y 7 8x 4y 4 9 12y 3x A 8 1 C 1 1 B 3 1 D No solution 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 All rights reserved 2 2 x 5 4 4 4 9 x y 5 5 6 8 9 y 0 44 0 2x 8y 4 1 y x 0 2 10 A 1 2 B 1 1 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

1 3 1 3 7 ut a System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 3 1 x 4 x 28 2y A 8 10 C 8 10 5 x A 7 10 C 4 10 15 9 2 2 0 44 8x 36y 7 8x 4y 4 9 12y 3x ftware LLC All rights reserved A 8 1 C 1 1 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 3 1 D No solution B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 2 6 8 5 4 4 4 9 x y 5 5 A 1 2 B 1 1 10 9 y 0 2 x 44 0 2x 8y 4 1 1 y x 0 2 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

Which two triangles are congruent by the AAS Theorem Complete the congrue statement H Z X

Which two triangles are congruent by the SSS Theorem Complete the congruence statement H A 111 G Z X Q

C 6 in 6 in What is the perimeter If necessary round to the nearest tent rhes

1 3 5 20 2 3 Kuta Software LLC All rights Systems by substitution Solve each system by substitution 1 2x 7y 1 7x y 20 A 3 1 B Infinite number of solutions C 3 1 D 3 1 3 x 7y 10 3x 7y 2 A 2 4 C 4 2 2x 2y 16 x 6y 8 A 8 2 B 8 0 C Infinite number of solutions D 8 3 7 y 6 6x 4y 6 A 5 6 C 5 6 B 4 2 D 4 2 9 8x 5y 23 3x 5y 12 B 5 6 D 5 2 A Infinite number of solutions B 1 3 C 1 3 D 3 1 2 6 4 8 10 reserved 2 8x 5y 1 y 3 A 2 3 C 6 3 4 3x 24y 3 x 8y 4 A No solution C 5 5 6 4x 3y 21 x 5y 12 A 3 5 C 3 3 8 8x5y 22 5x 3y 23 A 1 6 C 1 6 10 5x 4y 19 B 2 3 D 6 3 A 4 1 C 4 1 B 5 6 D 5 6 B 5 3 D 5 3 5x 2y 17 B 1 6 D 1 6 B 3 1 D 4 1

1 7 ut a System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 3 1 3 3 1 x 4 x 28 2y A 8 10 C 8 10 5 x A 7 10 C 4 10 15 9 2 2 0 44 8x 36y 7 8x 4y 4 9 12y 3x ftware LLC All rights reserved A 8 1 C 1 1 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 3 1 D No solution B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 2 6 8 5 4 4 4 9 x y 5 5 A 1 2 B 1 1 10 9 y 0 2 x 44 0 2x 8y 4 1 y x 0 2 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

C E G 3x 16 H 2x 50 F

97 cm a 72 cm What is the length of the missing leg If necessary round to the nearest ter centimeters