Practice and Applications

  1. 7.            

    A graph of a curve that oscillates about y = 0 with amplitude two-thirds, period 2 pi, and a maximum at (pi over 2, two-thirds).

  2. 9.

    A graph of a curve that oscillates about y = 0 with amplitude 2, period 2 pi, and a maximum at (pi, 2).

  3. 11.

    A graph of a curve that oscillates about y = 0 with amplitude 2, period 2 pi over 3, and which increases through (0, 0).

  4. 13.

    A graph of a curve that oscillates about y = 0 with amplitude 0.4, period pi over 2, and a minimum at (pi over 4, negative 0.4).

  5. 15.             

    A graph of a curve that oscillates about y = 0 with amplitude 3, period 6 pi, and a maximum at (3 pi, 3).

  6. 17.

    A graph of a curve that oscillates about y = 0 with amplitude 1, period 2, and a maximum at (one-half, 1).

  7. 19.

    A graph of a curve that oscillates about y = 0 with amplitude 5, period 4, and a maximum at (0, 5).

  8. 21.

    A graph of a curve that oscillates about y = 0 with amplitude 0.5, period 12, and a maximum at (3, 0.5).

  9. 23.

    A graph of a curve that oscillates about y = 0 with amplitude 12, period 5 pi over 6, and a minimum at (0, negative 12).

  10. 25.

    A graph of a curve that oscillates about y = 0 with amplitude 2, period pi over 2, and a maximum at (0, 2).

  11. 27.

    A graph of a curve that oscillates about y = 0 with amplitude 1, period 1, and which falls through (negative one-sixth, 0) and (eleven-sixths, 0).

  12. 29.

    A graph of a curve that oscillates about y = 0 with amplitude 8, period one-half, and a maximum at (one-eighth, 8).

  13. 31.

    A graph of curves that are periodic about the x-axis. One curve rises from x = negative pi with decreasing steepness, inflects at (0, 0), then rises and approaches x = pi.

  14. 33.

    A graph of parabolas that are periodic about the x-axis. A downward opening parabola is between x = 0 and x = pi and has a vertex at (pi over 2, negative 3).

  15. 35.

    A graph of a curve that oscillates about y = 2 with amplitude 0.5, period pi, and a maximum at (pi over 4, 2.5).

  16. 37.

    A graph of a curve that begins at (0, 3), to approximately y = 3.5, falls to (pi, negative 3), rises and inflects on the x-axis, then rises to (2 pi, 3).

  17. 39.

    A calculator graph of a curve that rises through (0, negative 1) to (1.5, 3), falls to (3.5, negative 1.5), rises to (5.5, negative 1), falls to (6.5, negative 1.5), then rises. All data are approximate.

  18. 41.

    A calculator graph of a curve that falls through (0, one-half) to (1, negative 0.75), rises to (2, negative one-half), falls to (3.5, negative 0.75), then rises to (5.5, 1.5). All data are approximate.

  19. 43.

    A calculator graph of a curve that rises through (negative 9, 0), falls to (negative 4, negative 0.25), rises to (0, 1), falls to (4, negative 0.25), rises through (6.5, 0), then falls through (9, 0). All data are approximate.

  20. 45.

    A calculator graph of a horizontal line that passes through (0, 1).

  21. 47. y = 2 sin(2x + π2)  

  22. 49. y = cos(π4 x − 3π4)

  23. 51.

    A calculator graph of a vertical ellipse centered at approximately (3, negative 1).

  24. 53.

    A calculator graph of a rightward opening parabola with a vertex at (negative 1, 0).

  25. 55.

    A calculator graph of a Lissajous curve.

  26. 57.

    A calculator graph of a repeating curve that rises from (0, negative 1) to (1, 1.5), falls to (2, 1), rises to (3, 1.5), then falls to (5, negative 5). All data are approximate.

  27. 59.

    A calculator graph of a curve that oscillates about y = 0 with amplitude 1, period pi, and a maximum at (negative pi over 4, 1). All data are approximate.

  28. 61. 4π

  29. 63. y = 3 sin x

    A graph of a curve that oscillates about y = 0 with amplitude 3, period 2 pi, and a maximum at (5 pi over 2, 3).

  30. 65. y = 3 cos 3x

    A graph of a curve that oscillates about y = 0 with amplitude 3, period 2 pi over 3, and a maximum at (0, 3).

  31. 67. y = 3 sin(πx + 0.25π)

    A graph of a curve that oscillates about y = 0 with amplitude 3, period 2, and a maximum at (0, 3).

  32. 69.

    A graph of a curve that rises from (0, 0) to (pi over 4, 10 to the fifth), then falls to (pi over 2, 0).

  33. 71.

    A graph of a curve that oscillates about y = 0 with amplitude 1130, period 0.02, and a maximum at (0, 1130).

  34. 73.

    A graph of a curve that is centered about i = 5 with amplitude 5, period 1 over 120 times s, and a minimum at (0, 0).

  35. 75.

    A graph of a curve that oscillates about y = 0 with amplitude 14, period 0.05, and a maximum at (0.025, 14).

  36. 77.

    A graph of a curve that begins at (0, 3.5), rises to (0, 3.9), falls to (15, negative 3.9), rises and inflects at (0, 20), rises to (30, 3.9), then falls through (40, 0). All data are approximate.

  37. 79. y = 67.5(1 − cosπt15)

    A graph of a curve that oscillates about y of m = 67.5 with amplitude 67.5, period 30, and a minimum at (30, 0).

  38. 81.

    A graph of a curve that begins at (0, 3), rising with increasing steepness.

  39. 83.

    A graph of a bell shaped curve that begins at (0, 9.4), rises to (6, 15.0), then falls to (12, 9.4).

  40. 85.

    A graph of a curve that oscillates about y = 0 with amplitude 5, period pi, and a maximum at (7 pi over 4, 5).

  41. 87.

    A graph of a curve that begins at (0, negative 0.75), rising and inflecting through (5, 0), rising to (18, 1.5), falls to (22, negative 1), then rising to (25, negative 0.75). All data are approximate.

  42. 89.

    A graph of a curve that begins at (0, 0), rises to (pi, 2), then falls to (2 pi, 0).

  43. 91.

    A graph of an upward opening parabola that falls through x = negative pi over 2, to vertex R on the Z-axis, then rises through x = pi over 2.

  44. 93.

    A graph of a curve that oscillates about q = 0.0009 with amplitude 0.0003 with period 0.0314.
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