The point is located eight units to the right of the y-axis and two units above the x-axis. A) ( 8, 2) B) (8, 2) C) ( 2, 8) D) (2, 8) E) ( 2, 8)

Transcription

1 Name: Date: 1. Find the coordinates of the point. The point is located eight units to the right of the y-axis and two units above the x-axis. A) ( 8, ) B) (8, ) C) (, 8) D) (, 8) E) (, 8). Find the coordinates of the point. The point is located six units to the left of the y-axis and is on the x-axis. A) (0, 0) B) (6, 0) C) (0, 6) D) ( 6, 0) E) (0, 6) 3. Determine the quadrant(s) in which (x, y) is located so that the condition is satisfied. xy > 0 A) quadrant I B) quadrant III C) quadrant IV D) quadrants II and IV E) quadrants I and III 4. Determine the quadrant(s) in which (x, y) is located so that the condition is satisfied. x = and y < 9 A) quadrant II B) quadrant IV C) quadrants I and IV D) quadrants II and IV E) quadrants III and IV Page 1

2 5. Sketch a scatter plot of the data shown in the table. 6. Find the length of each side of the right triangle and show that these lengths satisfy the Pythagorean Theorem. Show all of your work. Page

3 7. Find the distance between the points. (7, 1), (7, 3) A) B) 4 C) 14 D) 14 E) 0 8. Find the distance between the points. Round to the nearest hundredth, if necessary. (, 5), ( 1, 8) A) B) 4.4 C) 3.16 D) E) Find the midpoint of the line segment joining the points. (, 9), (, 1) A) (0, 4) B) (4, 0) C) (5, ) D) (, 5) E) (0, 4) 10. Given points (5, 3), (3, 1). Find a third point so that the three points form the vertices of an isosceles triangle. A) (14, 9) B) ( 5, 7) C) (13, 11) D) (4, ) E) (13, 7) Page 3

4 11. During math class, a fly lands on your graph paper. It lands at a point two units from the left side of the paper and two units from the bottom of the paper. Before it flies away, it walks in a straight line to a point three units from the left side of the paper and nine units from the bottom of the paper. How far did the fly walk? Round to the nearest unit. A) 9 units B) 7 units C) 8 units D) 6 units E) 49 units 1. The cost of a widget has increased from $4.83 in 00 to $6.13 in 004. Estimate the cost of a widget in 003 to the nearest cent. A) $10.31 B) $4.18 C) $5.48 D) $5.91 E) $5.99 Page 4

5 13. The polygon is shifted to a new position in the plane. Find the coordinates of the vertices of the polygon in its new position. A) B) C) D) E) none of these 14. A polygon has vertices with coordinates (6, 1), (11, 1), (6, 6), (1, 1). Find the coordinates of the vertices if the polygon is shifted 5 units down and units to left. A) (8, 4) (13, 6), (8, 1), (3, 6) B) (1, 3), (6, 1), (1, 8), ( 4, 1) C) (11, 1) (16, 3), (11, 4), (6, 3) D) (4, 6), (9, 4), (4, 11), ( 1, 4) E) (, 7), (9, 5), (, 5), ( 1, 5) Page 5

6 Average Price (dollars per gallon) 15. Use the graph below to answer the question. Approximate the percent increase in the price of a gallon of whole milk from 1999 to 005. Average U.S. Price for Whole Milk $3.30 $3.0 $3.10 $3.00 $.90 $.80 $.70 $.60 $.50 $ Year A) 6% B) 18% C) 1% D) 9% E) 0% Page 6

7 16. A pyramid has a square base measuring s = 54 meters on each side (see figure). The triangles making up the sides of the pyramid each have an altitude of d = 45 meters. Find the height of the pyramid in meters. d s A) 7 meters B) 196 meters C) 90 meters D) 36 meters E) 97 meters 17. The ordered pair,3 is a solution point for which equation below? A) x + 4 y B) y x + x 8 C) y x D) 1 3 y x + x E) x + 4 x y x 18. Find three ordered pairs satisfying y 4 x. A) 4,6, 5,18, 6, B) 4,14, 5,, 6, C) 4,14, 5,18, 6, D) 5,18, 6,30, 7,6 E) 5,18, 6,, 7,34 Page 7

8 19. Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation y x 4x. Plot at least 5 points along with the graph of the equation. A) B) Page 8

9 C) D) Page 9

10 E) Page 10

11 0. 4 Find the x- and y-intercepts of the graph of the equation y x 9x. A) x-intercepts: 0, 3, 0,3 ; y-intercept: 0,0 B) x-intercepts: 3,0, 0,0, 3,0 ; y-intercept: 0,0 C) x-intercepts: 3,0, 3,0 ; y-intercept: 0,0 D) x-intercepts: 3,0, 0,0, 3,0 ; y-intercepts: none E) x-intercepts: 0, 3, 0,0, 0,3 ; y-intercept: 0,0 Page 11

12 1. Assuming that the graph shown has y-axis symmetry, sketch the complete graph. A) B) C) Page 1

13 D) E) Page 13

14 . Given x y 9, use the algebraic tests to determine symmetry with respect to both axes and the origin. A) y-axis symmetry only B) x-axis symmetry only C) origin symmetry only D) x-axis, y-axis, and origin symmetry E) no symmetry 3. 3 x Given y, use the algebraic tests to determine symmetry with respect to both 4 x 1 axes and the origin. A) y-axis symmetry only B) x-axis symmetry only C) origin symmetry only D) x-axis, y-axis, and origin symmetry E) no symmetry Page 14

15 4. Use symmetry to sketch the graph of the given equation. A) B) C) D) Page 15

16 E) Page 16

17 5. Use a graphing utility to graph the equation and find all intercepts. Approximate any intercepts to the nearest hundredth if necessary. Use the standard graphing window size. A) B) x-intercept(s): none; y-intercept: (0, 5) C) x-intercept(s): none; y-intercept: (0, 5) D) x-intercept(s): ( 10, 0), (10, 0); y-intercept: (0, 5) E) x-intercept(s): none; y-intercept: (0, 5) x-intercept(s): none; y-intercept: none Page 17

18 6. Write the standard form of the equation of the circle whose radius is 6 and whose center is the point 1,. A) x y B) x y C) x y D) x y E) x y Write the standard form of the equation of the circle whose diameter has endpoints of 6,. 1, 10 and A) x y B) x+ 9 y+ 6 5 C) x y D) x y E) x 9 y Determine the center and radius of the circle represented by the equation x+ y A) 1 1 center:, 5 ; radius: 1 4 B) 1 1 center:, 5 ; radius: 1 16 C) 1 1 center:, 5 ; radius: 1 16 D) 1 1 center:, 5 ; radius: 1 4 E) 1 1 center:, 5 ; radius: 1 4 Page 18

19 9. A rectangular playground of length x and width y has a perimeter of 560 feet. Determine the equation for the area of the playground in terms of x. A) A 560x B) A 560x x C) A560 x D) A 80x x E) A80 x 30. Estimate the slope of the line. A) B) C) D) E) Page 19

20 31. Find the slope and y-intercept of the equation of the line. y 9 x A) 1 slope: ; y-intercept: 9 B) slope: 1 ; y-intercept: 9 C) slope: 9; y-intercept: D) slope: ; y-intercept: 9 E) slope: 9; y-intercept: 3. Find the slope and y-intercept of the equation of the line. y + 3x = 3 A) slope: 3; y-intercept: 3 B) slope: 3; y-intercept: 3 C) slope: 3; y-intercept: 1 D) slope: 3; y-intercept: 3 E) slope: 3; y-intercept: 3 Page 0

21 33. Plot the points and find the slope of the line passing through the pair of points. (, 1), (4, ) A) slope: 3 B) C) slope: 3 slope: 1 6 D) slope: 3 E) slope: 3 Page 1

22 34. Plot the points and find the slope of the line passing through the pair of points. (4, 3), ( 1, 3) A) slope: 0 B) slope: 1 C) slope: 5 D) 1 slope: 5 E) slope: undefined 35. Determine whether lines L 1 and L passing through the pairs of points are parallel, perpendicular, or neither. L 1 : ( 9, 9), (5, 3) L : ( 5, 3), ( 1, 9) A) parallel B) perpendicular C) neither 36. Determine whether lines L 1 and L passing through the pairs of points are parallel, perpendicular, or neither. L 1 : (5, ), ( 5, 9) L : (6, 8), ( 3, 6) A) parallel B) perpendicular C) neither Page

23 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Net profit (in thousands of dollars) 37. Determine whether lines L 1 and L passing through the pairs of points are parallel, perpendicular, or neither. L 1 : (4, 3), (8, 7) L : (9, 5), (1, 7) A) parallel B) perpendicular C) neither 38. The graph shows the net profit (in thousands) for Nguyen's catering business for the past year Month Use slopes to determine the month in which the net profit showed the least increase. A) February B) June C) July D) April E) January 39. Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope. point: (8, 3) slope: m = A) y = x 3 B) y = x + 14 C) y = x 19 D) y = x + 8 E) y = x + 11 Page 3

24 40. Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope. point: (9, 4) slope: m = = 0 A) y = x B) x = 4 C) y = 9 D) x = 9 E) y = Find the slope-intercept form of the line passing through the points. (4, 1), (5, 9) A) y 8x 4 B) y 8x + 31 C) 1 1 y x 8 D) 1 31 y x+ 8 8 E) y 8x Find the slope-intercept form of the line passing through the points. (3, ), ( 4, 3) A) 5 9 y x+ 7 7 B) 5 11 y x+ 7 7 C) 5 1 y x 7 7 D) 7 1 y x+ 5 5 E) 7 11 y x 5 5 Page 4

25 43. Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is x y 1, a 0, b 0. a b x-intercept: (, 0) y-intercept: (0, 5) A) 5x + y = 1 B) 1 5 x+ y 10 C) 1 x+ 5y 10 D) x + 5y = 10 E) 5x + y = Write the slope-intercept form of the equation of the line through the given point parallel to the given line. point: ( 7, 1) line: 36x 9y = 3 A) 1 43 y x B) 1 11 y x+ 4 4 C) y = 36x + 53 D) y = 4x 7 E) y = 4x Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: ( 4, 9) line: 7x 35y = 5 A) 1 59 y x 7 7 B) 1 49 y x 5 5 C) y = 5x + 11 D) y = 7x + 19 E) 9 y 5 x 5 Page 5

26 46. Gretel's Computer Repair Store purchases a network server for $498. The machine has a useful life of 6 years after which time another one will have to be purchased. Assume depreciation of the machine is linear. Write a linear equation giving the value V of the network server during the 6 years it will be in use. A) 1 V t6 83 B) 1 V t 6 83 C) 1 V t D) V = 83t E) V = 83t Does the table describe a function? Input value Output value A) yes B) no 48. Does the table describe a function? Input value Output value A) no B) yes 49. Does the table describe a function? Input value Output value A) yes B) no 50. Does the table describe a function? Input value Output value A) yes B) no Page 6

27 51. Which set of ordered pairs represents a function from P to Q? P = {, 4, 6, 8} Q = {, 0, } A) {(, ), (4, 0), (4, ), (6, 0), (8, )} B) {(6, ), (6, 0), (6, )} C) {(6, 0), (4, ), (, 0), (4, ), (6, )} D) {(4, 0), (6, ), (8, 0)} E) {(, ), (6, 0), (, ), (6, )} 5. Which equation does not represent y as a function of x? A) x = 5y 7 B) x = 8 C) y = 9x 7 D) y = 9x E) y 3 + 5x 53. Which equation does not represent y as a function of x? A) 4y = 0 B) x = 9y C) x 5y = 4 D) x + 4y = 8 E) 8y + 9x = Evaluate the function at the specified value of the independent variable and simplify. q (p) = 9p 9 q (1) A) 9p 81 B) 18 C) 0 D) p 9 E) p + 9 Page 7

28 55. Evaluate the function at the specified value of the independent variable and simplify. x, x1 f ( x) x + x, 1 x 1 3 x + x, x 1 f 1 5 A) 3 15 B) 1 10 C) 5 D) 7 5 E) Evaluate the function at the specified value of the independent variable and simplify. 3s f() s s 9 f (p + 4) A) 3 p 1 p 5 B) 3 p + 1 p 5 C) 3 s 1 s 5 D) 1 13 E) 1 5 Page 8

29 57. Find all real values of x such that f (x) = 0. f ( x) 81x 36 A) 3 B) 3 C) 4 9 D) 4 9 E) Find all real values of x such that f (x) = 0. 3 x f( x) A) 1 3 B) 1 3 C) 3 D) 3 E) Find the value(s) of x for which f (x) = g (x). f (x) = x 7x 3 g (x) = 9x 8 A) 8 3, 16, 9 B) 3, 7, C) 3, 5 D) 3, 5 E) 8 30, Page 9

30 60. Find the domain of the function. 7x f( x) x + 1 A) all real numbers x 1 B) all real numbers x 1, x 0 C) all real numbers D) x = 1, x = 0 E) x = Find the domain of the function. g( t) 4 t A) t B) t or t C) t 0 D) t E) all real numbers 6. Find the difference quotient and simplify your answer. f (s) = 8s + 9s, A) 17 + h B) s + s C) s + s D) 9 + 8h E) h f (4 h) f (4), h 0 h Page 30

31 63. A rectangle is bounded by the x-axis and the semicircle y 64 x (see figure). Write the area A of the rectangle as a function of x and determine the domain of the function. y 64 x (x, y) 8 8 A) A( x) x 64 x, 8 x 8 B) A( x) x 64 x, x 0 C) A( x) x 64 x, 8 x 8 D) A( x) x 64 x, all real numbers E) A( x) x 64 x, x 0 Page 31

32 64. Use the graph of the function to find the domain and range of f. A) B) C) D) E) Page 3

33 65. Use the Vertical Line Test to determine in which of the graphs y is not a function of x. A) x B) x C) x D) x E) All of the choices (A, B, C, and D) represent functions. Page 33

34 66. Find the zeroes of the functions algebraically. x + 9 x + 14 f( x) 6x A) 1 x = 7, x =, x 6 B) x = 7, x = C) 1 x 6 D) x = 7, x = E) 1 x = 7, x =, x Find the zeroes of the functions algebraically. f ( x) 5 x 3 A) 9 x 5 B) 9 x 5 C) 3 x 5 D) 3 x 5 E) no real zeroes 68. Use a graphing utility to graph the function and find the zeroes of the function. 6 f( x) 5 x A) 6 x 5 B) 5 x 6 C) 6 x 5 D) 5 x 6 E) no real zeroes Page 34

35 69. Determine the intervals over which the function is increasing, decreasing, or constant. A) B) C) D) E) Page 35

36 70. Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. A) B) C) D) E) Page 36

37 71. Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f (x) = x 3 x 3x 4 A) relative maximum: ( 0.54, 3.1) relative minimum: (1.87, 10.06) B) relative maximum: (1.87, 10.06) relative minimum: ( 0.54, 3.1) C) relative maximum: ( 3.1, 0.54) relative minimum: ( 10.06, 1.87) D) relative maximum: ( 10.06, 1.87) relative minimum: ( 3.1, 0.54) E) relative maximum: ( 10.06, ) relative minimum: ( 3.1, 44.50) 7. Graph the function and determine the interval(s) for which f (x) 0. f (x) = x + 3x A),0 3, B) 0,3 C) 0,3 D),0 3, E) {3} Page 37

38 73. Determine whether the function is even, odd, or neither. A) B) C) 74. Write the height h of the rectangle as a function of x. A) B) C) D) E) 75. Find the average rate of change of the function from x 1 to x. f (x) = x + 3 x 1 = 5, x = 7 A) B) 4 C) 4 D) 15 E) 1 Page 38

39 76. Use the position equation s = 16t + v 0 t + s 0 to write a function that represents the situation and give the average velocity of the object from time t 1 to time t. An object is thrown upward from a height of 67 feet at a velocity of 31 feet per second. t 1 = 1, t = 4 A) s 16t 31t 67 ; avg. velocity = 147 ft/s B) s 16t 31t 67 ; avg. velocity = 5 ft/s C) s 16t 31t 67 ; avg. velocity = 49 ft/s D) s 16t 67t 31; avg. velocity = 13 ft/s E) s 16t 67t 31; avg. velocity = 41 ft/s 77. Write the linear function f such that it has the indicated values. f( 5) = 3, f() = 9 A) 8 19 y x 7 7 B) 7 11 y x 8 8 C) 6 9 y x 7 7 D) 7 53 y x+ 6 6 E) 6 51 y x Evaluate the function for the indicated values. f ( x) 4 x (i) f (8) (ii) f ( 8.4) (iii) f A) (i) 71 (ii) (iii) 38 B) (i) 71 (ii) (iii) 4 C) (i) 70 (ii) 6 (iii) 4 D) (i) 70 (ii) 6 (iii) 38 E) (i) 70 (ii) (iii) Page 39

40 79. Which graph represents the function? A) B) C) D) E) Page 40

41 80. Which function does the graph represent? A) B) C) D) E) Page 41

42 81. Which graph represents the function? A) B) C) D) E) Page 4

43 Page 43

44 8. Which function does the graph represent? A) B) C) D) E) Page 44

45 83. A custodian is paid $8 per hour for regular time and time-and-a-half for overtime. The weekly wage function is given by 8 h, 0 h40 Wh ( ) 1( h 40) 30, h 40 where h is the number of hours worked in a week. The company increased its pay by 5 dollars per hour. What is the new weekly wage function? A) 8h 5, 0 h 40 Wh ( ) 17( h 40) 35, h 40 B) 8h 5, 0 h 40 Wh ( ) 19.5( h 40) 50, h 40 C) 13 h, 0 h40 Wh ( ) 17( h 40) 35, h 40 D) 13 h, 0 h40 Wh ( ) 17( h 40) 50, h 40 E) 13 h, 0 h40 Wh ( ) 19.5( h 40) 50, h 40 Page 45

46 84. Use the graph of f to determine which answer is the transformation. A) B) C) D) E) Page 46

47 85. Use the graph of to write an equation for the function whose graph is shown. A) B) C) D) E) Page 47

48 86. Describe the sequence of transformations from the related common function 3 f ( x) x to g. 3 g( x) 3( x 4) A) horizontal shift 4 units right; then vertical stretch by a factor of 3 B) horizontal shift 4 units left; then vertical stretch by a factor of 3 C) horizontal shift 4 units left; then vertical shrink by a factor of 3 D) vertical shift 4 units up; then vertical shrink by a factor of 3 E) vertical shift 4 units down; then vertical shrink by a factor of Describe the sequence of transformations from the related common function f ( x) to g. x g( x) x 6 A) reflection in the x-axis; then vertical shift 6 units down B) reflection in the x-axis; then vertical shift 6 units up C) reflection in the y-axis; then vertical shift 6 units up D) reflection in the y-axis; then horizontal shift 6 units right E) reflection in the y-axis; then horizontal shift 6 units left 88. Write an equation for the function that is described by the following characteristics: the shape of f ( x) A) g( x) x 5 B) g( x) x 5 C) g( x) x 5 D) g( x) x 5 E) g( x) x 5 x, but reflected in the y-axis, moved five units down Page 48

49 89. Write an equation for the function that is described by the following characteristics: the shape of f ( x) x, but moved two units down, three units to the left, and then reflected in the x-axis A) g( x) ( x 3) B) g( x) ( x 3) C) g( x) ( x 3) D) g( x) ( x ) 3 E) g( x) 3 ( x ) 90. Find ( f + g)(x). f (x) = 7x 4x 4 g(x) = 4x + 5x + 6 A) ( f + g)(x) = 11x 4 9x 10 B) ( f + g)(x) = 3x 4 + x + C) ( f + g)(x) = 11x 9x 10 D) ( f + g)(x) = 3x + x + E) ( f + g)(x) = 3x x 91. Find ( f g )(x). x 9 f( x) gx ( ) 7 x + 3 x A) x 9 ( f g)( x) 6 x + 3 B) x 60 ( f g)( x) 7 x + 3 C) x 66 ( f g)( x) 7 x + 3 D) x 63 x+ 7 ( f g)( x) 7 x + 3x E) x 63 x 7 ( f g)( x) 7 x + 3x Page 49

50 9. Find ( fg )(x). f ( x) 7x g( x) x 7 A) ( fg)( x) x x B) ( fg)( x) 7 x 14 + x C) ( fg)( x) 5 x 7 D) ( fg)( x) 14 x 7 E) ( fg)( x) 14 x + 49x 93. Find ( f g )(x). f ( x) x 3x g( x) 7 x A) x 3x ( f / g)( x), x 7 7 x B) x 3x ( f / g)( x), x 7 7 x C) x 3x ( f / g)( x), x 0 7 x D) x 3 ( f / g)( x), x 0 7 E) x ( f / g)( x) + 3, x Evaluate the indicated function for f (x) = x 7 and g (x) = x + 6. ( fg )(1) A) 4 B) 56 C) 41 D) 30 E) 54 Page 50

51 95. Evaluate the indicated function for f (x) = x 1 and g (x) = x +. ( f g )(t 8) A) t 17t + 69 B) t 17t + 73 C) t 15t + 69 D) t 15t + 73 E) t t Find f g. f (x) = x + 4 g (x) = x 7 A) ( f g)( x) x 10 B) ( f g)( x) x 3 C) ( f g)( x) x 10x 8 D) ( f g)( x) x + 11 E) ( f g)( x) x Find g f. f (x) = x + 6 g (x) = x A) ( g f )( x) x + 6 B) ( g f )( x) x 36 C) ( g f )( x) x + 36 D) ( g f )( x) x + 6x + 36 E) ( g f )( x) x + 1x + 36 Page 51

52 98. Find f g. f (x) = x + 4 gx ( ) A) 5 ( f g)( x) x B) 5 ( f g)( x) x + 8x C) 4 x + 1 ( f g)( x) x 16 D) 9 ( f g)( x) x 16 E) 4 x 59 ( f g)( x) x 16 x Find f g. f ( x) x 7 g( x) 1 x A) ( f g)( x) x x 6 B) ( f g)( x) x 6 C) ( f g)( x) 8 x D) ( f g)( x) 6 x E) ( f g)( x) 1 x 7 Page 5

53 100. Use the graphs of f and g to evaluate the function. f( x ) gx ( ) f g 3 A) 1 B) C) 4 D) 1 E) 101. The monthly cost C of running the machinery in a factory for t hours is given by C( t) 10t 100. The number of hours t needed to produce x products is given by t( x) 8 x. Find the equation representing the cost C of manufacturing x products. A) C( x) 80x 100 B) C( x) 80x 1000 C) C( x) 18x 100 D) C( x) 18x 110 E) C( x) 10x 108 Page 53

54 10. Find the inverse function of f ( x) 6 x + 4 A) x 4 gx ( ) 6 B) g( x) 4 x + 6 C) x + 4 gx ( ) 6 D) x gx ( ) 4 E) 1 g( x) x Find the inverse function of f ( x) x + A) 1/ g( x) x +, x 0 B) g( x) x +, x 0 C) g( x) x, x 0 D) g( x) x, x E) 1/ g( x) x, x Find the inverse function of f. 3 f ( x) x 1 A) 1 3 f ( x) x 1 B) 1 3 f ( x) x 1 C) 1 3 f ( x) x 1 D) 1 3 f ( x) x + 1 E) 1 3 f ( x) x + 1 Page 54

55 105. Find the inverse function of f. 9 x 6 9 f ( x), x 7 x A) 1 7x 9 3 f ( x), x 9 x 6 B) 1 7 x + 9 f ( x), x 9 x 6 3 C) 1 7 x + 9 f ( x), x 9 x 6 3 D) 1 9 x 6 9 f ( x), x 7x 9 7 E) 1 9 x f ( x), x 7x Determine whether the function has an inverse function. If it does, find the inverse function. f ( x) x + 1 A) No inverse function exists. B) f 1 ( x) x 1, x 0 C) f 1 ( x) x 1 D) f 1 ( x) x + 1, x 6 E) f 1 ( x) x 1 Page 55

56 107. Determine whether the function has an inverse function. If it does, find the inverse function. 9 x, x 3 f( x) x 3 + 5, x 3 A) No inverse function exists. B) x + 1, x 3 f ( x) 9 x 5 + 3, x 3 C) x + 1, x 5 f ( x) 9 x 5 + 3, x 5 D) x 1, x 5 f ( x) 9 x 5 + 3, x 5 E) x + 1, x 3 f ( x) 9 x, x x Use the functions given by f ( x ) 1 and 8 g( x) 3 x to find the indicated value. 1 g ( f ) (5) A) 3 4 B) 3 6 C) D) E) undefined Page 56

57 109. You have $1400 to invest in two accounts with simple interest rates of 8% and 4% per year, respectively. A model for the total interest I after the first year is I 0.08x 0.04(1400 x) where x is the number of dollars invested in the account with an interest rate of 8%. Find the inverse function, and determine the amount of money invested in the account with an interest rate of 8% when the total interest for the first year is $96. A) Inverse x5i 1400, amount invested $ 400 B) Inverse x5i 1400, amount invested $1000 C) Inverse x 5I 1400, amount invested $100 D) Inverse x 5I 1400, amount invested $500 E) Inverse x 0.08I 56, amount invested $ k Determine whether the variation model below is of the form y kx or y. x x y A) y kx B) k y x 111. k After determining whether the variation model below is of the form y kx or y, x find the value of k. x y A) k 7 B) 1 k 7 C) 7 k 3 D) 3 k 7 E) 7 k 78 Page 57

58 11. k After determining whether the variation model below is of the form y kx or y, x find the value of k. x y A) 1 k 4 B) k 3 C) 1 k 1 D) 5 k 4 E) 3 k 113. k Determine whether the variation model below is of the form y kx or y. x x y A) y kx B) k y x 114. Assume that y is directly proportional to x. If x 36 and y 7, determine a linear model that relates y and x. A) 4 y x 3 B) 3 y x 5 C) 3 y x D) 3 y x 4 E) y x 3 Page 58

59 115. The simple interest on an investment is directly proportional to the amount of the investment. By investing $5500 in a certain certificate of deposit, you obtained an interest payment of $ after 1 year. Determine a mathematical model that gives the interest, I, for this CD after 1 year in terms of the amount invested, P. I 0.04 P A) B) I 0.09 C) I 0.01 D) I E) I 0.06 P P P P 116. The sales tax on an item with a retail price of $74 is $1.7. Create a variational model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $3.58. A) $ B) $ C) $ D) $ E) $ The electrical resistance, R, of a wire is directly proportional to its length, l, and inversely proportional to the square of its diameter, d. A wire 15 meters long of diameter 5 millimeters has a resistance of 10 ohms. Find the resistance of a wire made of the same material that has a diameter of millimeters and is 0 meters long. A) R 1.5 ohms B) R 13.5 ohms C) R 13.8 ohms D) R 10 ohms E) R ohms Page 59

60 118. Find a mathematical model for the verbal statement: " t varies directly as the square of u and inversely as r." A) ku t r B) t ku r C) u t k r D) t k ur E) r t k u 119. Find a mathematical model for the verbal statement: A) B) C) D) E) Page 60

61 10. Find the constant of proportionality for the following situation: "y is jointly proportional to x and z and inversely proportional to w." w 9, x 6, y 5, and z 7 A) 35 k 54 B) 10 k 1 C) 15 k 14 D) 5 k 378 E) 14 k Find the constant of proportionality for the following situation: "y is jointly proportional to x and w." w3, x 8, and y 6 A) 16 k 9 B) 1 k 36 C) 1 k 1 D) 1 k 3 E) 18 k 3 1. Hooke's law states that the magnitude of force, F, required to stretch a spring x units beyond its natural length is directly proportional to x. If a force of 3 pounds stretches a spring from its natural length of 9 inches to a length of 9.7 inches, what force will stretch the spring to a length of 10.5 inches? Round answer to nearest hundredth. A) F 5.5 B) F 5.70 C) F 6.14 D) F 6.43 E) F 7.9 Page 61