Calculus - SUMMER PACKET NAME:__________________________
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Given 𝒇(𝒙) = 𝒙𝟐 − 𝟐𝒙 + 𝟓, find the following.
1. 𝑓(−2) = 2. 𝑓(𝑥 + 2) = 3. 𝑓(𝑥 + ℎ) =
Use the graph 𝒇(𝒙) to answer the following.
4. 𝑓(0) = 𝑓(4) =
𝑓(−1) = 𝑓(−2) =
𝑓(2) = 𝑓(3) =
𝑓(𝑥) = 2 when x = ? 𝑓(𝑥) = −3 when x = ?
Write the equation of the line meets the following conditions. Use point-slope form.
𝒚 − 𝒚𝟏 = 𝒎(𝒙 − 𝒙𝟏 )
5. slope = 3 and (4, −2) 6. 𝑚 = − and 𝑓(−5) = 7 7. 𝑓(4) = −8 and 𝑓(−3) = 12
MULTIPLE CHOICE!
17. Which of the following functions has a vertical asymptote at 𝑥 = 4 ?
(A)
(B)
(C)
(D)
(E) None of the above
18. Consider the function: (𝑥) = . Which of the following statements is true?
I. 𝑓(𝑥) has a vertical asymptote of 𝑥 = 2
II. 𝑓(𝑥) has a vertical asymptote of 𝑥 = −2
III. 𝑓(𝑥) has a horizontal asymptote of 𝑦 = 1
(A) I only
(B) II only
(C) I and III only
(D) II and III only
(E) I, II and III
𝟐
𝟏
Rewrite the following using rational exponents. Example: 𝟑 =𝒙 𝟑
𝒙𝟐
19. √𝑥 + √2𝑥 20. √𝑥 + 1 21.
√
22. − 23. + √𝑥 24. − 2 √𝑥 + 1
√ 𝒙𝟑 √
𝟐
𝟐 𝟏 𝟏
Write each expression in radical form and positive exponents. Example: 𝒙 𝟑 +𝒙 = 𝟑 +
𝒙𝟐 𝒙𝟐
25. 𝑥 −𝑥 26. 𝑥 +𝑥 27. 3𝑥
28. (𝑥 + 4) 29. 𝑥 +𝑥 30. 2𝑥 + 𝑥
Need to know basic trig functions in RADIANS! We never use degrees. You can either use the
Unit Circle or Special Triangles to find the following.
31. sin 32. cos 33. sin 2𝜋
34. tan 𝜋 35. sec 36. cos
37. sin 38. sin 39. tan
40. csc 41. sin 𝜋 42. cos
43. Find x where 0 ≤ 𝑥 ≤ 2𝜋, 44. Find x where 0 ≤ 𝑥 ≤ 2𝜋, 45. Find x where 0 ≤ 𝑥 ≤ 2𝜋,
1
sin 𝑥 = tan 𝑥 = 0 cos 𝑥 = −1
2
Solve the following equations. Remember 𝒆𝟎 = 𝟏 and 𝐥𝐧 𝟏 = 𝟎.
46. 𝑒 + 1 = 2 47. 3𝑒 + 5 = 8 48. 𝑒 =1
49. ln 𝑥 = 0 50. 3 − ln 𝑥 = 3 51. ln(3𝑥) = 0
52. 𝑥 − 3𝑥 = 0 53. 𝑒 + 𝑥𝑒 = 0 54. 𝑒 −𝑒 =0
Solve the following trig equations where 𝟎 ≤ 𝒙 ≤ 𝟐𝝅.
55. sin 𝑥 = 56. cos 𝑥 = −1 57. cos 𝑥 =
√
58. 2sin 𝑥 = −1 59. cos 𝑥 =
√
60. cos =
√
61. tan 𝑥 = 0 62. sin(2𝑥) = 1 63. sin =
√
For each function, determine its domain and range.
Function Domain Range
64. 𝑦 = √𝑥 − 4
65. 𝑦 = (𝑥 − 3)
66. 𝑦 = ln 𝑥
67. 𝑦 = 𝑒
68. 𝑦 = √4 − 𝑥
Simplify.
Maisy
69.
√ 70. 𝑒 71. 𝑒
Y x
Excel
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