Standardized Test Prep

SAT/ACT

48. Which expression equals 5 x x 2 − 9 − 4 x x 2 + 5 x + 6 ? fraction 5 x , over x squared , minus 9 end fraction . minus . fraction 4 x , over x squared , plus 5 x plus 6 end fraction . question mark
    1. 7 x ( x − 3 ) ( x + 3 ) ( x + 2 ) fraction 7 x , over open , x minus 3 , close . open , x plus 3 , close . open , x plus 2 , close end fraction
    2. x 2 − 2 x ( x − 3 ) ( x + 3 ) ( x + 2 ) fraction x squared , minus 2 x , over open , x minus 3 , close . open , x plus 3 , close . open , x plus 2 , close end fraction
    3. x 2 + 22 x ( x − 3 ) ( x + 3 ) ( x + 2 ) fraction x squared , plus 22 x , over open , x minus 3 , close . open , x plus 3 , close . open , x plus 2 , close end fraction
    4. 9 x 2 − 2 x ( x − 3 ) ( x + 3 ) ( x + 2 ) fraction 9 , x squared , minus 2 x , over open , x minus 3 , close . open , x plus 3 , close . open , x plus 2 , close end fraction

49. Which of the relationships is represented by the graph below?

    

    6. y = log 4 ( x − 1 ) + 5 y equals , log base 4 , open x minus 1 close plus 5
    7. y = log 4 ( x − 1 ) − 2 y equals , log base 4 , open x minus 1 close minus 2
    8. y = log 4 ( x + 2 ) − 2 y equals , log base 4 , open x plus 2 close minus 2
    9. y = log 4 ( x − 1 ) − 1 y equals , log base 4 , open x minus 1 close minus 1
50. What is a simpler form of 2 x − 5 6 x − 3 ? fraction 2 over x , minus 5 , over 6 over x , minus 3 end fraction . question mark
    1. 2 − 5 x 6 − 3 x fraction 2 minus 5 x , over 6 minus 3 x end fraction
    2. 2 + 5 x 6 − 3 x fraction 2 plus 5 x , over 6 minus 3 x end fraction
    3. 2 x − 5 6 x + 3 fraction 2 x minus 5 , over 6 x plus 3 end fraction
    4. 6 + 3 x 2 − 5 x fraction 6 plus 3 x , over 2 minus 5 x end fraction
51. What word makes the statement “The domain and range of a(n) ________________ function is the set of all real numbers” sometimes true?
    6. polynomial
    7. logarithmic
    8. exponential
    9. quadratic

Short Response

52. What is the least common denominator for the rational expressions 1 x 2 − 5 x − 6 fraction 1 , over x squared , minus 5 x minus 6 end fraction  and 1 x 2 − 12 x + 36 ? fraction 1 , over x squared , minus 12 x plus 36 end fraction . question mark  Show your work.

Mixed Review

See Lesson 8-4.

Divide. State any restrictions on the variable.

53. 3 x 2 − 9 x x − 2 ÷ x 2 − 9 4 x − 8 fraction 3 , x squared , minus 9 x , over x minus 2 end fraction . divides . fraction x squared , minus 9 , over 4 x minus 8 end fraction
54. 3 x − 6 12 x − 24 ÷ x 2 − 5 x + 6 3 x 2 − 12 fraction 3 x minus 6 , over 12 x minus 24 end fraction . divides . fraction x squared , minus 5 x plus 6 , over 3 , x squared , minus 12 end fraction
55. 5 x + 15 10 x − 10 ÷ x 2 + 6 x + 9 3 x 2 − 3 fraction 5 x plus 15 , over 10 x minus 10 end fraction . divides . fraction x squared , plus 6 x plus 9 , over 3 , x squared , minus 3 end fraction

See Lesson 7-4.

Write each logarithmic expression as a single logarithm.

56. log 3 y + 4 log 3 t log base 3 , y plus 4 , log base 3 , t
57. 7 log p + 2 log q 7 log p plus 2 log q
58. log 5 x − 1 5 log 5 y log base 5 , x minus , 1 fifth . log base 5 , y

See Lesson 6-6.

Let f ( x ) = x 2 + 1 f open x close equals , x squared , plus 1  and g ( x ) = 3 x . g open x close equals 3 x .  Evaluate each expression.

59. ( g ◦ f ) ( − 3 ) open g composition f close open negative 3 close
60. ( f ◦ g ) ( − 3 ) open f composition g close open negative 3 close
61. ( g ∘ f ) ( 1 2 ) open , g composition f , close . open , 1 half , close
62. ( f ◦ f ) ( 3 ) open f composition f close open 3 close

Get Ready! To prepare for Lesson 8-6, do Exercises 63-65.

See Lesson 1-4.

Solve each equation. Check your answers.

63. − 3 ( x − 4 ) = 2 ( x + 8 ) negative 3 open x minus 4 close equals 2 open x plus 8 close
64. 0.2 ( x + 8 ) − 3.4 = 2.4 0.2 open x plus 8 close minus 3.4 equals 2.4
65. x 2 + x 3 = 15 x over 2 , plus , x over 3 , equals 15

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