C Challenge

Graph each function. Include a dashed line for each asymptote.

45. g ( x ) = x x − 1 g open x close equals . fraction x , over x minus 1 end fraction
46. y = 1 ( x − 1 ) 2 y equals . fraction 1 , over open , x minus 1 , close squared end fraction
47. y = 2 ( x − 2 ) ( x + 2 ) y equals . fraction 2 , over open , x minus 2 , close . open , x plus 2 , close end fraction
48. y = 1 x 2 − 2 x y equals . fraction 1 , over x squared , minus 2 x end fraction
49. Graph f ( x ) = ( x + 2 ) ( x + 1 ) x + 2 f open x close equals . fraction open , x plus 2 , close . open , x plus 1 , close , over x plus 2 end fraction  and g ( x ) = x + 1 . g open x close equals x plus 1 .  Are the graphs the same? Explain.

Standardized Test Prep

SAT/ACT

50. A caterer spends $75 on sliced cheese. As a bonus, he receives 1 lb of sliced cheese free with his order. What equation gives the caterer's cost y per pound of cheese as a function of the total number of pounds x of cheese the caterer receives?
    1. y = 75 x + 1 y equals . fraction 75 , over x plus 1 end fraction
    2. y = 75 x − 1 y equals . fraction 75 , over x minus 1 end fraction
    3. y = 75 x + 1 y equals , 75 over x , plus 1
    4. y = 75 x − 1 y equals , 75 over x , minus 1
51. Which is an equation of the line with the same y-intercept but half the slope of the line y = 4 − 10 x ? y equals 4 minus 10 x question mark
    6. y = − 5 x + 4 y equals negative 5 x plus 4
    7. y = 2 − 10 x y equals 2 minus 10 x
    8. y = 2 − 5 x y equals 2 minus 5 x
    9. y = − 5 x − 2 y equals negative 5 x minus 2
52. How many x-intercepts does the graph of y = x 2 + 7 x + 11 y equals , x squared , plus 7 x plus 11  have?
    1. 0
    2. 1
    3. 2
    4. 3
53. Which expression is equivalent to 4 x 2 + 24 + 36 2 x 2 + 4 x − 6 , fraction 4 , x squared , plus 24 plus 36 , over 2 , x squared , plus 4 x minus 6 end fraction . comma  where x ≠ 1 x not equal to 1  and x ≠ − 3 ? x not equal to negative 3 question mark
    6. 2 x + 6 x − 1 fraction 2 x plus 6 , over x minus 1 end fraction
    7. 2 x 2 + 6 x + 6 2 , x squared , plus 6 x plus 6
    8. x + 3 x − 1 fraction x plus 3 , over x minus 1 end fraction
    9. 2 x + 4 2 x plus 4

Extended Response

54. The drama club plans to attend a professional production. From 10 to 35 students will go. Each ticket costs $25 plus a $2 surcharge. There is a one-time handling fee of $3 for the entire order of tickets. Write a linear function that models this situation. What domain and range are reasonable for the function?

Mixed Review

See Lesson 11-6.

Suppose y varies inversely with x. Write an equation for the inverse variation.

55. y = 4 when x = 5 y equals 4 , when , x equals 5
56. y = − 1 when x = 8 y equals negative 1 , when , x equals 8
57. y = 1 2 y equals , 1 half  when x = 24
58. y = 7  when  x = − 6 y equals 7 , when , x equals negative 6

See Lesson 9-6.

Find the number of real-number solutions of each equation.

59. x 2 + x + 1 = 0 x squared , plus x plus 1 equals 0
60. − 3 x 2 + 4 x = − 5 negative 3 , x squared , plus 4 x equals negative 5
61. 2 x 2 + 5 = 0 2 , x squared , plus 5 equals 0
62. 9 x 2 + 144 = 7 x 9 , x squared , plus 144 equals 7 x

Get Ready! To prepare for Lesson 12-1, do Exercises 63–66.

See Lesson 1-5.

Find each sum or difference.

63. − 7 . 2 + 8 . 9 negative 7 . 2 plus 8 . 9
64. 8 . 7 − ( − 4 . 4 ) 8 . 7 minus open negative 4 . 4 close
65. 16.2 + 4.95
66. − 10 . 25 − ( − 5 . 35 ) negative 10 . 25 minus open negative 5 . 35 close

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