Standardized Test Prep

SAT/ACT

46. Which function represents the value after x years of a new delivery van that costs $25,000 and depreciates 15% each year?
    1. y = − 15 ( 25 , 000 ) x y equals negative 15 . open 25 comma 000 close to the x
    2. y = 25 , 000 ( 0.15 ) x y equals 25 comma 000 . open , 0.15 , close to the x
    3. y = 25 , 000 ( 0.85 ) x y equals 25 comma 000 . open , 0.85 , close to the x
    4. y = 25 , 000 ( 1.15 ) x y equals 25 comma 000 . open , 1.15 , close to the x
47. What is f ( x ) = 3 x 1 3 f open x close equals 3 , x super 1 third end super  for x = 1 125 ? x equals , 1 over 125 . question mark
    6. 15
    7. 3 5 3 fifths
    8. 3 3 5 fraction cube root of 3 , , over 5 end fraction
    9. 5 3 3 5 , cube root of 3 ,
48. What is the simplified form of 2 + i 2 − i ? fraction 2 plus i , over 2 minus i end fraction . question mark
    1. − 1 negative 1
    2. 3 + 4 i 3 fraction 3 plus 4 i , over 3 end fraction
    3. 5 + 4 i 5 fraction 5 plus 4 i , over 5 end fraction
    4. 3 + 4 i 5 fraction 3 plus 4 i , over 5 end fraction
49. Which graph represents the equation y = x 2 − x − 2 ? y equals , x squared , minus x minus 2 question mark
    6. 
    7. 
    8. 
    9. 

Extended Response

50. You are driving a car when a deer suddenly darts across the road in front of you. Your brain registers the emergency and sends a signal to your foot to hit the brake. The car travels a reaction distance D, in feet, during this time, where D is a function of the speed r, in miles per hour, that the car is traveling when you see the deer, given by D ( r ) = 11 r + 5 10 . d open r close equals . fraction 11 r plus 5 , over 10 end fraction . .  Find the inverse and explain what it represents. Is the inverse a function?

Mixed Review

See Lesson 6-8.

Graph each function.

51. y = 3 − 2 x + 2 y equals 3 minus 2 , square root of x plus 2 end root
52. y = 3 2 x − 1 3 y equals 3 . cube root of 2 x minus 1 end root ,
53. y = − 2 + y equals negative 2 plus   x square root of x

See Lesson 4-4.

Factor the expression.

54. 8 + 27 x 3 8 plus , 27 x cubed
55. 3 x 2 + 11 3 x squared , plus 11 x − 4 negative 4
56. 25 − 40 x + 16 x 2 25 minus 40 x plus , 16 x squared

See Lesson 3-6.

Solve the system of equations using a matrix.

57. { x + 5 y = − 4 x + 6 y = − 5 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 5 y equals negative 4 , row2 column 1 , x plus 6 y equals negative 5 , end table
58. { 3 a + 5 b = 0 a + b = 0 left brace . table with 2 rows and 1 column , row1 column 1 , 3 eh plus 5 b equals 0 , row2 column 1 , eh plus b equals 0 , end table
59. { − x + 2 y + z = 0 y = − 2 x + 3 z = 3 x left brace . table with 3 rows and 1 column , row1 column 1 , negative x plus 2 y plus z equals 0 , row2 column 1 , y equals negative 2 x plus 3 , row3 column 1 , z equals 3 x , end table

See Lesson 7-1.

Get Ready! To prepare for Lesson 7-2, do Exercises 60–63.

Graph each function.

60. y = 3 x y equals , 3 to the x
61. y = 4 ( 2 ) x y equals 4 . open 2 close to the x
62. y = 0 . 75 x y equals 0 . , 75 to the x
63. y = 0.5 ( 4 ) x y equals 0.5 . open 4 close to the x

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