MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) Evaluate the function for the given value of x. p(x) = x, q(x) = x - 9, (p q)(x) =? ) A) (p q)(x) = x - 9, x 9 B) (p q)(x) = x - 9, x 0 C) x + x - 9, x 0 D) (p q)(x) = x - 9 x, x 0 2) Find (f + g)(x). f (x) = x 2 and g(x) = -7 A) (f + g)(x) = (x - 7) 2 B) (f + g)(x) = x 2-7 C) (f + g)(x) = 49 D) (f + g)(x) = x ) 3) Evaluate the function for the given value of x. f (x) = 7x, g(x) = -5x 2 + 4, ( f - g)(x) =? A) ( f - g)(x) = 5x 2 + 7x - 4 B) ( f - g)(x) = 5x 2-7x + 4 C) ( f - g)(x) = 5x 2 + 7x + 4 D) ( f - g)(x) = 5x 2-7x - 4 3) 4) Find f g (x). 4) A) f (x) = x and g(x) = x - 9 f g (x) = x - 9 x 2 + 4, x 9 f B) g (x) = x2 + 4 x - 9 C) f g (x) = x2 + 4 x - 9, x 9 f D) g (x) = x - 9 x ) Find ( f + g)(3) for the given functions. f (x) = - + x 2 g(x) = 2x + A) 5 B) 48 C) x 2 + 2x D) 4x 2 + 4x + 0 5)

2 6) A chemist wants to mix a 22% acid solution with a 46% acid solution to get 32 L of a 37% acid solution. How many liters of the 22% solution and how many liters of the 46% solution should be mixed? A) 2 L of the 22% solution; 20 L of the 46% solution B) 20 L of the 22% solution; 2 L of the 46% solution C) 9 L of the 22% solution; 3 L of the 46% solution D) 3 L of the 22% solution; 9 L of the 46% solution 7) Paula invested into two accounts; one pays 4% simple interest and the other pays 5% simple interest. She invested $000 more in the account paying 5% than in the account paying 4%. At the end of the first year, Paula's total return was $950. How much did she invest in each account? A) $2,000 at 4%; $9000 at 5% B) $0,000 at 4%; $,000 at 5% C) $9000 at 4%; $2,000 at 5% D) $,000 at 4%; $0,000 at 5% 6) 7) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 8) The population of a country, y (in millions), can be approximated by the relation y = 0.27x + 35 where x represents the number of years since ) a. Approximate the population of the country in the year b. In what year will the population of the country reach approximately 36,270,000? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 9) The following table describes the temperature (y) inside an oven, in degrees, x minutes after it was turned on. 9) Temp. (y) Minutes (x) What is the domain of this relation? A) (72, 33, 86, 237, 285, 333, 379, 425} B) {0,, 2, 3, 4, 5, 6, 7, 8, 9} C) [0, 9] D) [72, 425] 2

3 0) The table gives a relation between the month of the year and the average precipitation for that month for Miami, Florida. What is the range element corresponding to November? 0) Month x Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Precipitation (in.) y A) 6.42 B) 2.29 C) 2.66 D) 7.30 ) A plane flew 800 miles in 4 hours with the wind. It took 5 hours to travel the same distance against the wind. What is the rate of the plane in still air and the rate of the wind? A) plane: 90 mph; wind: 20 mph B) plane: 200 mph; wind: 60 mph C) plane: 90 mph; wind: 30 mph D) plane: 80 mph; wind: 20 mph 2) The perimeter of a triangle is 43 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 3 cm less than the sum of the other two sides. Find the lengths of the sides. A) 5 cm; 9 cm; 9 cm B) 4 cm; 9 cm; 20 cm C) 3 cm; 20 cm; 20 cm D) 3 cm; 9 cm; 2 cm ) 2) 3) m(x) = x +, n(x) = x + 2, (m n)(x) =? 3) A) (m n)(x) = x B) (m n)(x) = x + 3 C) (m n)(x) = (x + 2) x + D) (m n)(x) = x ) n(x) = x -, p(x) = x 2-5x, (p n)(x) =? 4) A) (p n)(x) = x 2-7x - B) (p n)(x) = x 2-7x + 6 C) (p n)(x) = x 2-5x - D) (p n)(x) = x 2-5x + 6 5) r(x) = -4x - 2, n(x) = x + 4, (r n)(x) =? 5) A) (r n)(x) = -4x + 2 B) (r n)(x) = -4x - 8 C) (r n)(x) = -4x + 8 D) (r n)(x) = -4x

4 6) Determine if the relation defines y as a function of x. 6) A) Function B) Not a function 7) Which relation is NOT a function? 7) A) {(7, 7), (9, 9), (5, 5), (0, 0)} B) {(7, 9), (9, 5), (-7, 5), (5, 9)} C) {(7, 9), (0, 5), (9, 7), (7, 5)} D) {(-7, 2), (3, 9), (0, 9), (5, 9)} 8) Determine if the function is constant, linear, quadratic, or none of these. z(x) = 3 + 2x 2 + 3x A) Constant B) Quadratic C) Linear D) None of these 9) Determine if the function is constant, linear, quadratic, or none of these. t (x) = - x A) Linear B) Constant C) Quadratic D) None of these 8) 9) 20) Which of the following is a constant function? 20) A) f (x) = 03 B) f (x) = 20x C) f (x) = 32x 2 D) f (x) = 9 x SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 2) Write the relation as a set of ordered pairs. 2) Town Population Springfield 85,000 Shelbyville 55,000 Capital City 900,000 4

5 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 22) List the domain and range. x y A) Domain {-4, -8, 2, -6}; range {8, 0, 2,, 7} B) Domain {-4, -8, 2, -6); range {8, 0, 2,, 7, } C) Domain {-4, -8, 2, -6, -8, 2}; range {8, 0, 2,, 7, } D) None of the above 22) 23) Find the range of the relation. Use interval notation where appropriate. 23) A) { 20, 0, 0, 0, 5} B) {0, 20, 40, 20} C) [ 20, 5] D) [ 40, 20] 5

6 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 24) Write the relation as a set of ordered pairs. 24) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 25) Consider the points plotted below. a. Write the relation as a set of ordered pairs. b. Determine the domain and range. 25) A) a. {( 4, 3), ( 3, 2), ( 2, 4), (, ), (2, 4), (3, )} b. Domain: [ 4, 3] range: [ 4, 4] B) a. {( 4, 3), ( 3, 2), ( 2, 4), (, ), (2, 4), (3, )} b. Domain: { 4, 3, 2,, 2, 3} range: { 4, 2,,, 3, 4} C) a. {( 4, 2), ( 2, 3), (, 3), (, ), (3, 4), (4, 2)} b. Domain: { 4, 2,,, 3, 4} range: { 4, 3, 2,, 2, 3} D) a. {( 4, 2), ( 2, 3), (, 3), (, ), (3, 4), (4, 2)} b. Domain: [ 4, 4] range: [ 4, 3] 6

7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 26) Find the domain and range of the relation. Use interval notation where appropriate. 26) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 27) Find the domain of the function. Write your answer in interval notation. g(y) = y - 6 A) (6, ) B) (-, ) C) [6, ) D) (-, 6) (6, ) 28) Find the domain. Write the answer in interval notation. g(x) = x 2 + 2x - 48 A) (-, -8) (6, ) B) (-8, 6) C) (-, ) D) (-, -8) (-8, 6) (6, ) 29) Find the domain. Write the answer in interval notation. m(x) = x - 3 x A) (-, -9] [-9, ) B) [-, -9) (-9, ] C) (-, ) D) (-, -9) (-9, ) 27) 28) 29) 7

8 30) For what value(s) of x is f (x) = 2? 30) A) x = -2 B) x = -3 C) x = 3 D) x =.5 3) Find the x- and y-intercepts of the function. B(x) = 2x + 5 A) x- and y-intercept: (0, 0) 3) B) x-intercept: - 2, 0 ; y-intercept: (5, 0) 5 C) x-intercept: - 5, 0 ; y-intercept: (0, 5) 2 D) x-intercept: - 5, 0 ; y-intercept: (0, -5) 2 32) Find the x- and y-intercepts of the function. g(x) = -0x ) A) x-intercept: 0, ; y-intercept: (-6, 0) B) x-intercept: (0, -6); y-intercept: (26, 0) C) x- and y-intercept: (0, 0) D) x-intercept: - 8, 0 ; y-intercept: (0, -6) 5 8

9 33) Find the x- and y-intercepts of the function. h(x) = - A) x-intercept: none; y-intercept: (0, -) B) x-intercept: (-, 0); y-intercept: none 33) C) x-intercept: none; y-intercept: (-, 0) D) x-intercept: (0, -); y-intercept: none 34) If f (x) = 3x 2 + 8x - 0, find and simplify f (2 + x). 34) A) 3x 2 + 2x + 8 B) 3x 2 + 8x - 2 C) 8 + x D) 3x x + 8 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 35) If K(x) = x x, find K(). 35) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 36) If h(m) = m 3 + 6m 2 + 7m - 7, find h(-k). 36) A) h(-k) = -k 3-6k 2-7k + 7 B) h(-k) = -m 3 + 6m 2-7m - 7 C) h(-k) = -k 3-6k 2-7k - 7 D) h(-k) = -k 3 + 6k 2-7k - 7 9

10 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 37) In the next week, Maureen plans to work at most 50 hours, divided between 2 jobs. Let x represent the number of hours spent as a telemarketer, and let y represent the number of hours spent working as a lifeguard. Find a set of inequalities to describe the constraints on Maureen's work time. 37) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 38) In the next week, Maureen plans to work at most 50 hours, divided between 2 jobs. Let x represent the number of hours spent as a telemarketer, and let y represent the number of hours spent working as a lifeguard. Is the point (-2, 5) in the feasible region defining Maureen's work time? A) Yes B) No 38) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 39) Graph the solution set of the inequality. 3y 2x > 0 39) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 40) Which is a solution of 5x + 3y 9? 40) A) (, 0) B) (5, 7) C) (0, 4) D) (5, 0) 4) Match each equation with its graph. 4) f(x) = x g(x) = x h(x) = x 3 I II III A) f(x), II; g(x), III; h(x), I B) f(x), III; g(x), II; h(x), I C) f(x), I; g(x), III; h(x), II D) f(x), III; g(x), I; h(x), II 0

11 42) Set up the augmented matrix. -9x + 3y = - -9x - 6y = -7 42) A) B) C) D) ) Determine if the matrix is a row matrix, a column matrix, a square matrix, or none of these A) column matrix B) square matrix C) row matrix D) none of these 43) 44) Set up the augmented matrix. -4x - = -2z -8x + 6z = 8 + 7y 2x + 4y - 2z = 5 44) A) B) C) D) ) Determine if the matrix is a row matrix, a column matrix, a square matrix, or none of these. 45) A) square matrix B) column matrix C) row matrix D) none of these

12 46) Graph the constant function f (x) = -2. Then use the graph to identify the domain and range of f. A) Domain: (-, ); range: {-2} B) Domain: {-2}; range: (-, ) 46) C) Domain: {-2}; range: (-, ) D) Domain: (-, ); range: {-2} 47) m(x) = x 2, r(x) = 6, (m r)(4) =? 47) x - 4 A) 6 B) 0 C) 9 4 D) Undefined 48) f (x) = 2x, g(x) = x - 4, A) f g (-) = 2 5 f g B) (-) =? 48) f g (-) = 5 2 C) f g (-) = D) f g (-) =

13 49) f (x) = 4x, g(x) = x - 3, (f g)(-4) =? 49) A) (f g)(-4) = 28 B) (f g)(-4) = -2 C) (f g)(-4) = 9 D) (f g)(-4) = 2 50) f (x) = -3x, g(x) = A) (f - g)(-2) = C) (f - g)(-2) = - 3 5, (f - g)(-2) =? 50) x - 3 B) (f - g)(-2) = 3 5 D) (f - g)(-2) = ) Determine which point is the solution to the given system. 5) y = 7 2 x - 30 y = 3 5 x - A) (8, -2) B) (5, 8) C) (2, 2) D) (0, 5) 52) The graph of a system of linear equations is given. Identify the number of solutions to the system. 52) -2x + 5y = 5 y = 2 5 x + A) one solution B) zero solutions C) infinite number of solutions 3

14 53) The graph of a system of linear equations is given. Identify whether the system is consistent or inconsistent. 2x - 5y = 4 4y = 3x + 53) A) inconsistent B) consistent 54) Which one of the following points is a solution to the system? 5x + 6y + 3z = 7x + 2y + 9z = -3 6x + 3y + 4z = A) (, -3, -2) B) (8, -3, -7) C) (8, -6, -) D) All three points are solutions to the system. 55) Solve the system. -4x + 8y = 4 x = 2y - 54) 55) A) 0, 2 B) (9, 5) C) Infinitely many solutions; (x, y) y = 2 x + 2 ; dependent system D) No solution; { }; inconsistent system 4

15 56) Solve the system by the addition method. -4x + 4y = x = y A) (7, 9) B) (3, 5) C) Infinitely many solutions; (x, y) y = 2 7 x D) No solution; { }; inconsistent system 57) Solve the system by the addition method. 2 x + y = x + 2y = -9.9 A) Infinitely many solutions; (x, y) y = - 2 x B) (0, -4.95) C) No solution; { }; inconsistent system D) (0, -.8) ; dependent system ; dependent system 56) 57) 58) Solve the system. If there is no unique solution, label the system as either dependent or inconsistent. -0.2x - 0.3y = y - 0.z = x + 0.3z = 4.2 A) (2, -4, -) B) (9, -4, -) C) (9, -4, 0) D) Dependent system (infinitely many solutions) 58) 5

16 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 59) Solve the system of equations by graphing. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. 59) y = 3 2 x + 3x = 2y - 3 6

17 60) Solve the system of equations by graphing. 60) y = 3 x + 4 y = 2 3 x + 5 6) Solve the system of equations by graphing. 2x - y = 6 3x - 5y = 6 6) 7

18 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 62) Given the matrix M -2 2 M = write the matrix obtained by multiplying the first row by -5 and then adding the first row to the second row. A) C) B) D) ) 63) Solve the system by using the Gauss-Jordan method. x + 3y = -2-4x - 2y = 8 A) (-5, ) B) (-8, 2) C) (-2, 0) 63) D) Infinitely many solutions; (x, y) y = - 3 x ; dependent system 64) Given the matrix R - 0 R = write the matrix obtained after executing the following elementary row operations: 64) i). First, multiply the first row by -2 and add the result to the second row. ii). Then, multiply the first row by - and add the result to the third row. A) C) B) D)

19 65) Solve the system of equations. 0x + 20z = 82 y + 2z = 2 x - 5y = A) 5, - 6 5, 8 5 B) 5, 3, 8 5 C) 4, 3, 0 D) (0, -4, 6) 5 65) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 66) Graph the solution set of the compound inequality. 3y < x 7 and x > 5 67) Graph the solution set of the compound inequality. x + y > 5 or y 8 66) 67) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 68) Solve the system by the addition method. 5x = -9y - 2-5y = 4x + 9 A) (-6, ) B) (-5, 6) C) (-, -3) D) (3, -4) 69) Solve the system by the addition method. -6x - 2y = 22-7x + 4y = 32 A) (-6, 7) B) (0, 8) C) (-4, ) D) (-2, -5) 70) Solve the system by the addition method. -9x - 4y = 6 2x + 4y = -6 A) (-4, -2) B) (0, -4) C) (-4, 5) D) (4, -3) 7) Solve by using the substitution method. y = -3x x - 6y = -24 A) (5, 5) B) (4, 8) C) (7, -) D) No solution; { }; inconsistent system 68) 69) 70) 7) 9

20 72) Solve the system by using the substitution method. 72) x = y y = x A) (7, -7) B) (-3, ) C) (2, -3) D) (-8, 5) 73) Solve the system by using the substitution method. y = 500x y = -350x A) (7, 340) B) (, -2660) C) (5, 040) D) (6, -60) 73) 74) Is the graph below the graph of a function? 74) A) No B) Yes 75) Is the graph below the graph of a function? 75) A) Yes B) No 20

21 76) Is the graph below the graph of a function? 76) A) No B) Yes 2

22 Answer Key Testname: TEST2REV2 ) D 2) B 3) A 4) C 5) A 6) A 7) B 8) a. 35,635,000; b. The year 200 9) B 0) C ) D 2) B 3) B 4) B 5) B 6) B 7) C 8) B 9) D 20) A 2) { (Springfield, 85,000), (Shelbyville, 55,000), (Capital City, 900,000) } 22) A 23) D 24) {(a, 52), (b, 3), (c, 0), (d, 3)} 25) B 26) Domain: (-, ) Range: [0, ) 27) C 28) C 29) C 30) B 3) C 32) D 33) A 34) D 35) 9 36) D 37) x 0 y 0 x + y 50 38) B 22

23 Answer Key Testname: TEST2REV2 39) 40) A 4) C 42) C 43) B 44) B 45) D 46) D 47) D 48) D 49) B 50) B 5) D 52) C 53) B 54) B 55) C 56) D 57) C 58) B 59) No solution; { }; inconsistent system 23

24 Answer Key Testname: TEST2REV2 60) 6) 62) D 63) D 64) D 65) A 66) 24

25 Answer Key Testname: TEST2REV2 67) 68) A 69) C 70) B 7) B 72) C 73) A 74) A 75) A 76) A 25