Question 1(Multiple Choice Worth 3 points)

(02.02 MC) How many solutions does the system of equationsx?y= ? 2 andy= (2x+ 3)²? 2 have?

Infinitely

many

0

1

2

Question 2(Multiple Choice Worth 3 points)

(02.03 MC) Givenf(x) =x²+ 6x+ 8 andg(x) =x³+ 2x²?x? 2, find the domain of

{x? ?|x? ?2, ?1, 1} {x? ?|x? ?1, 1} {x? ?|x? ?4} {x? ?}

Question 3(Multiple Choice Worth 3 points)

(02.03 MC) The Scooter Company manufactures and sells electric scooters. Each scooter cost $200 to produce, and the company has a fixed cost of $1,500. The Scooter Company earns a total revenue that can be determined by the functionR(x) = 400x? 2x², wherexrepresents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?

?2x²+ 200x? 1,500 ?2x²? 200x? 1,500 ?2x²+ 200x? 1,100 ?400x³? 3,000x²+ 80,000x+ 600,000

Question 4(Multiple Choice Worth 3 points)

(02.04 MC) Given the following table with selected values of the functionsf(x) andg(x), determinef(g(2)) ?g(f(?1)).

x	?3	?2	?1	0	1	2
f(x)	16	13	?2	?5	?11	?20
g(x)	?10	?3	1	14	8	0

?8

?5

?2

1

Question 5(Multiple Choice Worth 3 points)

(02.01 LC) The graphs ofandg(x) = ?log₂(x+ 3) have which of the following features in common?

x?Intercept Range

y-Intercept

Vertical

asymptote

Question 6(Multiple Choice Worth 3 points)

(02.02 MC) The elimination method was used to solve the following system of equations: x? 6y= 30 5x? 2y= ?46 Which of the following is the correct y-coordinate of the solution?

?12

?7

7

12

Question 7(Multiple Choice Worth 3 points)

(02.02 LC) The equationsx+y= 6 andare represented in the graph. Determine the solution(s) to the system of equations.

(2, 4) and (?6, 0) (2, 4) and (6, 0) (?2, ?4) and (?6, 0) (?2, ?4) and (6, 0)

Question 8(Multiple Choice Worth 3 points)

(02.03 MC) Given various values of the linear functionsf(x) andg(xin the table, determine the y-intercept of (f?g)(x).

x	?6	?4	?1	3	4
f(x)	?36	?26	?11	9	14
g(x)	15	11	5	?3	?5

(0, 9) (0, 3) (0, ?3) (0, ?9)

Question 9(Multiple Choice Worth 3 points)

(02.03 MC) The volume of a rectangular prism box can be represented by the functionV(x) = 2x³? 7x²+ 3x. If the height of the box isxcm, which of the following can represent the length and width of the container?

2x+ 1 andx+ 3 2x+ 1 andx? 3 2x? 1 andx+ 3 2x? 1 andx? 3

Question 10(Multiple Choice Worth 3 points)

(02.04 MC) Determine the domain of (g?f)(x) iff(x) =x²+ 3x? 5 and

{x? ?} {x? ?|x? ?4, ?1, 1} {x? ?|x? ?4, 1} {x? ?|x? ?1}

Question 11(Essay Worth 10 points)

(02.02 HC) A railroad's track can be determined using the following graph. Several different roadways are in the same region as the railroad. Part A:A highway's path can be found using the equation 2x + 3y = 21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the highway, and explain completely. (5 points) Part B:A turnpike's route is determined by the equationProve algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary work. (5 points)

Question 12(Essay Worth 10 points)

(02.03, 02.04 HC) An ice cube is freezing in such a way that the side lengths, in inches, iswheretis in hours. The surface area of the ice cube is the functionA(s) = 6s². Part A:Write equation that gives the volume at t hours after freezing begins. (2 points) Part B:Find the surface area as a function of time, using composition, and determine its range. (4 points) Part C:After how many hours will the surface area equal 294 square inches? Show all necessary calculations, and check for extraneous solutions. (4 points)

(Screenshot of questions 12-1)

Question 1(Multiple Choice Worth 3 points) (02.02 MC) How many solutions does the system of equations x - y = - 2 and y = (2x + 3)2 - 2 have? O Infinitely many Oo 01 O2 Question 2(Multiple Choice Worth 3 points) (02.03 MC) Given f (x) = x2 + 6x + 8 and g(x) = x3 + 2x2 - x - 2, find the domain of _ (x). O{xER x#-2, -1, 1} OfxE R x # -1, 1} O(x ER| x #-4} OfxE R}Question 3(Multiple Choice Worth 3 points) (02.03 MC) The Scooter Company manufactures and sells electric scooters. Each scooter cost $200 to produce, and the company has a fixed cost of $1,500. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x - 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit? O-2x2 + 200x - 1,500 O-2x2 - 200x - 1,500 O-2x2 + 200x - 1, 100 O-400x3 - 3,000x2 + 80,000x + 600,000Question 4(Multiple Choice Worth 3 points) (02.04 MC) Given the following table with selected values of the functions f (x) and g(x), determine f (g(2)) - g(f (-1)). -3 2 f (x) 16 13 -2 -5 -11 -20 g(x) -10 -3 1 14 8 0 O-8 O-5 O-2 O1Question 5(Multiple Choice Worth 3 points) (02.01 LC) f(x) g(x) ' -10 9 8 -7 6 -5 -4 -3 -2-1 3 4 5 6 7 8 9 10 The graphs of f(x) = 1x3and g(x) = -log2(x + 3) have which of the following features in common? 20 Ox-Intercept O Range O y-Intercept O Vertical asymptoteQuestion 6(Multiple Choice Worth 3 points) (02.02 MC) The elimination method was used to solve the following system of equations: x - 6y = 30 5x - 2y = -46 Which of the following is the correct y-coordinate of the solution? O-12 -7 07 O 12Question 7(Multiple Choice Worth 3 points) (02.02 LC) The equations x + y = 6 and y = = X- 6 x -3 are represented in the graph. Ty 10 -10 -9 8 7 6 5 4 -3 -2 1 2 3 4 6 7 8 9 1 Determine the solution(s) to the system of equations. O (2, 4) and (-6, 0) O (2, 4) and (6, 0) O (-2, -4) and (-6, 0) O (-2, -4) and (6, 0)Question 8(Multiple Choice Worth 3 points) (02.03 MC) Given various values of the linear functions f (x) and g(x in the table, determine the y-intercept of (f - g)(x). 2 f (x) 36 -26 -119 g(xx) 15 11 5 -3 -5 O (0, 9) O (0, 3) O (0, -3) O (0, -9) Question 9(Multiple Choice Worth 3 points) (02.03 MC) The volume of a rectangular prism box can be represented by the function V(x) = 2x3 - 7x2 + 3x. If the height of the box is x cm, which of the following can represent the length and width of the container? O 2x + 1 and x + 3 O 2x + 1 and x - 3 O 2x - 1 and x + 3 O 2x - 1 and x - 3Question 10(Multiple Choice Worth 3 points) (02.04 MC) Determine the domain of (go f)(x) if f (x) = x- + 3x - 5 and g(x) = - 1 x +1 OfxE R} OfxER x #-4, -1, 1} O{xER| x # -4, 1} OfxER| x #-1}Question 11 (Essay Worth 10 points) (02.02 HC) A railroad's track can be determined using the following graph. 10 - N W -10 9 8 7 6 5 4 3 2 -10 1 2 3 4 5 6 7 9 10 -1 Several different roadways are in the same region as the railroad. Part A: A highway's path can be found using the equation 2x + 3y = 21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the highway, and explain completely. (5 points) Part B: A turnpike's route is determined by the equation y = _x2. Prove algebraically how many intersections there will be between the railroad and the tumpike, showing all necessary work. (5 points)Question 12 (Essay Worth 10 points) (02.03, 02.04 HC) An ice cube is freezing in such a way that the side length s, in inches, is s(f) = -/+4, where f is in hours. The surface area of the ice cube is the function A(S) = 652. Part A: Write an equation that gives the volume at t hours after freezing begins. (2 points) Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points) Part C: After how many hours will the surface area equal 294 square inches? Show all necessary calculations, and check for extraneous solutions. (4 points)