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Name ______________________________________________ Date __________________________________Thurgood Marshall Academy Public Charter High School – Pre-Calculus

Midterm Review

1.1 Determine whether or not an ordered pair is a solution of a two-variable equation by substitution.

1. Is (−3 ,−4 ) a solution of 6 y−2x=−10?

2. Is (−4 ,−3) a solution of x2−3 xy− y2=−29?

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Perfect or near perfect: _____ Practice more if time: _____ Need more practice: _____

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1.2 Complete an ordered pair so that it is a solution of a two-variable equation by substitution and equation-solving.

3. Determine an ordered pair whose y-coordinate is 3 that is a solution of y=−2x−5.

4. (w ,−4) is a solution of x= y2−3 y . Find w .

5. ( 38 ,m) is a solution of x+ y=78 . Find m.

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2.1 Generate ordered pairs that are solutions of a two-variable equation by educated selection, substitution, and equation-solving.

6. Generate five solutions of y=23x+1.

7. Generate five solutions of x= y3+ y .

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3.1 Explain why a graph could not be the graph of a given two-variable equation by selecting and substituting ordered pairs that are not solutions.

8. Explain, with reference to a specific ordered pair, why the given graph could not be the graph of 2 x− y=4.

9. Explain, with reference to a specific ordered pair, why the given graph could not be the graph of y=x2+4 x+5.

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3.2 Draw a portion of the graph of a two-variable equation by generating a sufficient number of ordered pairs.

10. Generate and plot at least 5 solutions of x= y2−3 y .

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4.1 Complete an ordered pair given graphically by substitution into a given two-variable equation.

11. The graph of y=3 √x+3−6 is shown. Find the coordinates of P.

12. The graph of y=(1+x)3+1 is shown. Find the coordinates of Q.

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5.1 Determine the intercepts of a relation described by a two-variable equation by substituting zero for the appropriate variable.

13. Find all intercepts of y=−4 x+12.

14. Find all intercepts of y=4 (x−3)(x−2).

15. Find all intercepts of y=√x+49.

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8.1 Sketch a relation of the form y=xa for positive integer values of a by generating ordered pairs that satisfy the equation and extrapolating about the end behavior.

16. Draw a sketch of y=x5 . Include the coordinates of at least 5 ordered pairs in your picture.

17. Draw a sketch of y=x4 . Include the coordinates of at least 5 ordered pairs in your picture.

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9.1 Describe the end behavior of a power function given its equation.

18. Describe the end behavior of y=x10 .

19. Describe the end behavior of y=x55 .


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9.2 Describe the probable end behavior of a function given graphically or in a table.

Describe the probable end behavior of the relation whose graph is shown.

20. 21. 22.

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10.1 Explain why a relation (given graphically or in a list) is not a function.

Explain, with reference to specific ordered pairs, why the given relation is not a function.

23. {(−4 ,2 ) , (7 ,16 ) , (8 ,16 ) ,(−4 ,−2)}

24.

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11.1 Given a two-variable equation, answer questions about its solutions posed in function notation.

25. Suppose g contains the ordered pairs satisfying 3 x−2 y=6. Find g (8 ).

26. f is the function containing all of the ordered pairs satisfying y=−4 x−3. Find x so that f ( x )=9.

27. Suppose f contains the ordered pairs satisfying y=x3+x2+ x. Find f (−3 ).

28. Suppose h contains the ordered pairs satisfying y=23x+4. Find x so that f ( x )=6.


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12.1 Given a function graph and a number c, find f (c ) or find all values of x for which f ( x )=c.

Suppose the following is the graph of f.

29. Find f (2). 30. Find f (−2.5).

31. Find all x such that f ( x )=1. 32. Find all x such that f ( x )=−1.

33. Find all x such that f ( x )=3. 34. Find all x such that f ( x )=5.


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13.1 Use interval notation to describe values of x on which a function, given graphically, is positive, negative, or zero.

16.1 Use interval notation to describe values of x on which a function is increasing, decreasing, or constant.

Suppose the following is the graph of f.

35. For what values of x is f (x) positive? 36. For what values of x is f (x) increasing?

37. When is f (x) decreasing? 38. When is f (x) negative?

39. Where is f (x) zero? 40. Where is f (x) constant?


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14.1 Perform sign analysis to determine when an expression is positive, negative, or zero.

Perform sign analysis for each expression.

41. (x+3)(x−5)

42. (x+2)( x+2)(x−4)

43. x (x−2)(x+2)


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15.1 Answer questions about functions whose equations are given using function notation.

44. Generate three solutions of h ( x )=√15−x .

45. Find all intercepts of f ( x )=2(x+5)(x−5).

46. Describe the end behavior of m (x )=x3.

47. Suppose q ( x )=−3 x+2. Find m such that q (m)=−7.

48. Suppose g ( x )=−3 x2. Find g(2).


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17.1 State when a polynomial function, given as an equation, is positive, negative, or zero using sign analysis.

49. When is f ( x )=(x+3)(x−2) positive?

50. When is f ( x )=(x−3)(x−3)(x−5) negative?

51. When is f ( x )=−3(x−5)(x−1) negative?


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17.2 Sketch the graph of a polynomial function using sign analysis.

52. Sketch the graph of f ( x )=(x+3)(x−1)(x−4).

53. Sketch the graph of f ( x )=(x+4)(x+4)(x−3)(x−5).


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18.1 Find zeros of functions.

54. Find all zeros of f ( x )=3 x−12.

55. Find all zeros of f ( x )=(x+3)(x−2).

56. Name all zeros of the function whose graph is shown.

57. Suppose f is the function whose ordered pairs satisfy 2 x−5 y=20. Find all zeros of f.


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18.2 Draw conclusions about polynomial functions using the Factor Theorem.

58. Suppose you know that −4 is a zero of a polynomial function. What conclusion can you draw about the

function using the Factor Theorem?

59. Suppose you know that (x−3) is a factor of a polynomial function. What conclusion can you draw about the


60. Suppose you know that x is a factor of a polynomial function. What conclusion can you draw about the function

using the Factor Theorem?

61. Suppose you know that −4 and 5 are zeros of a polynomial function. What conclusion can you draw about the



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18.3 Write a factored polynomial function for a given graph.

Write a polynomial function equation for each graph.

62.

63.

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19.1 Sketch vertical translations of functions.

64. The graph of y=f (x ) is shown. Sketch y=f ( x )+3

65. Sketch f ( x )=√x−5. 66. Sketch y=x2−6.


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19.2 Write the equation of a function that has undergone a vertical translation.

Write an equation for each graph.

67. 68. 69.

70. Suppose the thin graph is the graph of y=f (x ). Write the equation of the thick graph.


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20.1 Given a function graph, state the domain, range, and extreme values.

Suppose the following is the graph of f. Suppose the following is the graph of g.

71. What is the domain of f? 72. What is the range of f?

73. What is the maximum value of f? 74. What is the minimum value of f?

75. What is the domain of g? 76. What is the range of g?

77. What is the maximum value of g? 78. What is the minimum value of g?


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20.2 State domain, range, and extreme values of parent functions (power functions, absolute value function, square root function) and vertical translations of those functions.

79. State the domain of f ( x )=|x|.

80. State the domain of f ( x )=√x.

81. State the range of f ( x )=x2.

82. State the range of f ( x )=x3.

83. State the domain of f ( x )=|x|+5.

84. State the range of f ( x )=x3−1.

85. State the minimum value of f ( x )=√x+4.


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Review skills – rounding

86. Round 45,693 to the nearest hundred.

87. Round 658,238 to the nearest thousand.

88. Round 56.983 to the nearest hundredth.

89. Round 89.2935 to the nearest thousandth.

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Review skills – fraction operations

Simplify.

90.25+ 16 91.

25−16

92.25∙ 16 93.

25÷ 16


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Review skills – mixed number operations

94. 2 12∙1 35 95. 2 1

2+1 35

96. 2 12÷1 35 97. 2 1

2−1 35

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Review skills – percent and fraction of a number


98. What is 13 of 24?

99. 6 is 20% of what number?

100. What is 40% of 25?

101. 18 is 34 of what number?

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