Algebra Questions

Exit Ticket 11 6 Which of the following is an expression that represents The sum of twice x and 10 a 2x 10 b 2 x 10 c 2x 10 d 2 x 10

2 If y 8 what is the value of four times the quotient of y and 2

2 For f x x and g x x 4 find the following composite functions and state the domain of each a fog b gof c fof d gog c f of x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice O A The domain off of is x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed O B The domain of f of is all real numbers d gog x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice O A The domain of g og is x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed

Evaluate each expression using the values given in the table 1 2 3 6 0 2 02 1 4 X f x g x a fog 1 d gof 3 a fog 1 b fog 2 c gof 2 d gof 3 e gog 1 f fof 3 3 2 10 8 4 1 0 1 4 2 0 b fog 2 e g o g 1 c gof 2 f fof 3

Evaluate the expression 1331 2 3 Select the correct choice below and fill in any answer boxes in your c O A 2 3 1331 Simplify your answer

Rewrite the following radical with a rational exponent 3 7x 3

Rewrite 1 2 3 27 with positive exponents and completely simplify if possible Select the correct choice below and fill in any answer boxes in your choice O A 1 27 2 3 B The solution is not a real number Simplify your answer Type an integer or a fraction

Rewrite 32 O A 1 2 5 Select the correct choice below and fill in any answer boxes in your choice with positive exponents and completely simplify if possible 1 2 5 11 Simplify your answer Type an integer or a fraction 32 OB The solution is not a real number

Use a calculator to write 7 as a decimal

ewrite following radical with a rational exponent 6 X

Use a calculator to find 25 251 1 5 Jound th 1 5 root hundredth

3 Solve the following system y x 6 x 5 y x

9 88 p 41p 64p 18 p 84p 48p 51p 83p A 136p 106p 103p 40p B 136p 106p 13p 40p C 125p 101p 13p 40p D 125 p 106p 13p 40p 10 23 73 11 8 42r 36 51 15 A 44 77 88 74 B 44r 31 88r 74 C 10 88 74 D 444 33 88 74 11 x 5x 2x 2x 8x A 3x 10x 6x B 3x 10x x C 5x 10x x D 3x 10x 2x 12 12 7v 4 8v 2v A 15v 4 B 22 4 4 C 15v 3 4 D 22y 3y 4

8 92x 92x 59x 42x 40x 18x 42x 98x A 73x 59x 60x 190x 42x B 132x 59x 60x 190x 42x C 99x 59x 60x 190x 42x D 160x 59x 60x 190x 42x 9 88 p 41 p 64p 18p 84p 48 p 51p 83p A 136p 106p 103p 40p B 136p 106p 13p 40p C 125p 101p 13p 40p D 125p 106p 13p 40p

For each pair of equations state if there is one solution no solution or infinite solutions a 27x 24y 18 and 9x 8y 6 b y 3x 8 and y 3x 8 c 4x 20y 28 and x 5y 7

8 92x 92x 59x 42x 40x 18x 42r 98r A 73x 59x 60x 190x 42x B 132x 59x 60x 190x 42x C 99x 59x 60x 190x 42x D 160x 59x 60x 190x 42x 9 88 p 41p 64p 18 p 84p 48p 51 p 83p A 136p 106p 103p 40p B 136p 106p 13p 40p C 125 p 101p 13p 40p D 125p 106p 13p 40p 10 23 73 112 8r 422 36r 1 15r A 447 77 88 74 B 44 31 88 74 C 10 77 88 74

10 23 73 11 8r 42r 36r 51 15r A 44 77 88 74 B 44r 31 88r 74 C 10r 77r 88r 74 447 33 88 74 11 x 5x 2x 2x 8x A 3x510x 6x B 3x10x x C 5x 10x x D 3x10x 2x 12 12 7v 4 8v 2v A 154 4 B 22v 4 4 C 15v 3 4 D 22v 3 4

5 3v 7v 6 v 8v A 6 3 6 B 6v 9 6 C 6v 9 10 D 6v 5 61 6 6 4x 7x 3x 7x 6x A 10x 13x 4x B x 13x 4x C x 16x 4x D 3x 13x 4x 7 30 14r 22 41r 77 26 75r 70r A 185r 100 73r 41r 33 B 89r 100r 73r 41r 33 C 89r 100r 26 41 55 D 89 100 73 41 55

1 3 Simplify each difference 1 8x 8 8x 8 8x 7x A 23x 14 C 15x B 23x 6 D 23x Simplify each expression 3 4 3a 7a 7 8a A 5a 17 B 5a 7a 17 C 5a 7a 12 D Sa 7a 11 k 2 4 2 8 8r 7 6r 1 A 10 7 C 6 7 B 6 2r 7 D 6r 3r 7 4 8a a 5a 3a 7a A 5a 11a 2a B 5a 19a 3a C 5a 11a 3a D a 11a 2a

3 5 Simplify each expression 3 4 3a 7a 7 8a A 5a 17 B 5a 7a 17 C 5a 7a 12 D 5a 7a 11 5 3v 7v 6v v 8v A 64 3 62 B 6v 9 6v C 6v 9v D 6 5 6v 4 10v 4 6 4 8a a 5a 3a 7a A 5a 11a 2a B 5a 19a 3a C 5a 11a 3a D a 1la 2a 6 4x 7x 3x 7x 6x A 10x 13x 4x B x 13x 4x C x 16x 4x D 3 13 4x

Waterworks is a company that manufactures and sells paddleboards Its profit P in hundreds of dollars earned is a function of the number of paddleboards sold x measured in thousands Profit is modeled by the function P x 4x 68x 168x What do the zeros of the function tell you about the number of paddleboards that Waterworks should produce Com In order to make a profit Waterworks must produce more than and fewer than paddleboards

Factor the following polynomial using the difference of squares 42 81

A business owner receives a 5 000 loan with 13 interest charged at the end of each year Write an equation to represent the amount owed in dollars after the t years of making no payments Use your equation to determine the amount of the loan after 4 years

Determine the zeroes for the following polynomial function Write your answers as integers or fractions in order from least to greatest f x x x 3 2z 1

A computer costs 800 It loses 1 4 of its value every 2 years after it is purchased How much will the computer be worth in 6 years

When a zero root has an even multiplicity the graph When a zero root has an odd multiplicity the graph the the ec bounces on raxis raxis x y

13 8 pts Use the rational function g x below to answer the following draw a sketch of the graph a Domain b y Intercept c x Intercept s d Vertical Asymptotes e Horizontal Asymptotes g x 2x 12 x 4 y 14 4 pts Determine the solution set to the following rational inequality 5r 2 x 4 0

In 1985 there were 285 cell phone subscribers in the small town of Centerville The number of subscribers increased by 75 per year after 1985 How many cell phone subscribers were in Centerville in 1994

which functions are invertible Select each correct answer S 10 8 6 4 10 8 6 4 2 s 8 do t 4 2 64 84 104 O of 6 the 2 60 61 Po N 12 6 8 10 9 x 8 10 X 10 8 6 10 8 6 4 2 2 10 8 6 4 2 2 4 6 8 10 64 8 do 8 6 4 No 6 10 XA K XA 6 8 10

20 dAR 0 45155 05057 0s0s A OB www OC O D O

An adult takes 400 mg of ibuprofen Each hour the amount of ibuprofen in the person s system decreases by about 29 How much ibuprofen is left after 6 hours nswer to a Different problem 3 mL

This set of points is on the graph of a function 3 9 1 1 0 0 2 4 Which points are on the graph of the inverse Select each correct answer 4 2 0 0 O 1 1 O 9 3

What is the inverse of f x 2x 3 O f x 2x 3 O f x 2x 3 o f x x 1 20 f x 1 x 13 1

What is the inverse of f x x 5 for a 5 where function g is the inverse of function f O g x x 5 x 5 O g x x 5 x 0 O g x x 5 x 5 O g x x 5 x 0

What is the inverse of the function g x x 2 3 g x x 2 g x x 1 3 0 g x x 2 1 Oq x x 2

1 Sketch the graph of each linear inequality 1 3x y 2 A B C D 2 K 2 x 2y 0 A B C D

6 5 pts Use synthetic division to divide g x by x 3 and then w g x d x f x r x g x 10x 14x 13 2x g x

11 use th x x 12 pt Give the equation s of all vertical asymptotes of h x Vertical Asymptotes 10 1 pt Determine the x intercept s of h x Write as an ordered pair x intercepts 11 1 pt Determine the y intercept of h x Write as an ordered pair y intercept h x g x 12 3 pts Determine the horizontal asymptotes of the following functions If there is no horizontal asymptote answer with None 6x h x 12x 1800 3x 19 6x 12x 1800 3x 19 j x 6x 1 12x 1800 3x 19

Answer the constructed response questions completely Include all parts Show all work Write in complete sentences Use the equation builder when necessary Remember Only original work will be accepted Do your own work Do not search the internet for the answer Do not copy and paste work that is not your own Part A A function f x is transformed into the function g x 2 x 4 5 Name and explain in complete sentences the transfor that occurred to the parent cube root function Part B How is the DOMAIN of a cube root function different from the DOMAIN of a square root function Use complet

Solve each system by elimination 1 3x 4y 3 12x 2y 12 3 6x 18y 24 7x 9y 2 5 3x 3y 3 8x 10y 22 2 6x 6y 6 3x y 17 4 6x 5y 5 7x 7y 0 6 7x 9y 27 8x 5y 15

ach system by substitution or 3x 8y 22 x y 118 3x 22 3 x 18 88 66 la bb T F 6 y 2x 6 x 3y 17 x 3 2x 6 17 6 18 1 6 y 11 6 6 y 5 Sx 18 12 118 117 7 8 Sx 35 SS 7y 3 x 8y 15 0x 1869 24 4x6x 105 x 81 7 8 x 4 elimination y 2 6 181 9 14 8x 6y 10 6x 7y 15 16 18 saj ly 3 45 74 3 45 45 7x y 14 14x 4y 28 24 42 7 y 6x 5 2x 4y 20

Solve each system by elimination 7 2x 8y 2 4x 2y 4 9 10x 7y 27 5x 2y 8 11 6x 9y 12 7x 10y 10 8 x 14y 10 3x 7y 5 10 7x 10y 27 3x 3y 9 12 9x 8y 6 2x 3y 30

4x 5y 6 y 4 1 6 4x 52 4x 6 6 y 2 4x 20x 30 1 20x 20 24 30 6 3 5x 2y 2 0 15x 10y 30 2 Sox 20 20 30x 4y 60 32x 32 5 4x 4y 165 7 3x 5y 28 4 30 30 1 2 242 24 40 20 X 2 20x 20y 40 12x2y 11 192 32 X 6 24 x 11 mination 5 2 2y 2 10 2y 2 10 2 61 9 61 2 16 21 4 4 6 4y X6 28 44 16 24 78 8y 2 y 4x Ay 16 6x 3y 15 6 y x 11 8x 3y 21 4x 3y 10 8x 10

Solve each system by substitution or 7 4x 7y 171 x 2y 5 4 4 79 1 4 89 20 7 3 9 5x 5y 10 y 6x 19 5x s 6x 14 0 Sx 30x 5 10 3SX 95 0 43 45 30 38 34 9 9 135x 005 x 3 200 elimination 11 Ax 10y 28 5 5x 4y 16 4 px soy 140 5X 357 2 6y 3 1 SX 0 S S X 8 8 y 3x 5 7x 3y 9 10 9x 6y 15 8x 5y 12 12 9x 6y 24 18x 7y 28

Let p and q represent the following statements p It is Tuesday q I am working Write the compound statement p q in words Choose the correct answer below Next question OA If it is Tuesday then I am working OB If it is Tuesday then I am not working OC I am working if and only if it is not Tuesday OD It is not Tuesday if and only if I am not working www

Let p represent the following statement p Saturn is the only planet with rings Express the symbolic statement p in words In words the symbolic statement p is which of the following A Saturn is often the only planet with rings OB Saturn is a planet with rings OC Neptune is the only planet with rings D Saturn is not the only planet with rings

Let p and q represent the following simple statements p The chair is broken q I eat bananas Write the following compound statement in its symbolic form If the chair is not broken then I do not eat bananas Choose the correct symbolic form below Op q p q p q p q www

Let p and q represent the following statements p The vest is tan q The shoe is black Write the compound statement p q in words Choose the correct answer below A The vest is not tan and the shoe is black OB The vest is tan and the shoe is black OC If the vest is not tan then the shoe is black D The vest is not tan or the shoe is black Next question www

Let p and q represent the following statements p One does one s best q Red and yellow make purple Express the following statement symbolically One does not do one s best Symbolically the statement is www

Consider the statements p The hat is tan q The vest is red Rewrite the statement PAq in English What is the English version of the statement p q A If the hat is not tan then the vest is red OB The hat is tan and the vest is red OC The hat is not tan or the vest is red D The hat is not tan and the vest is red