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14.1

14.1. Trig. Graphs. Find the amplitude and period for . Then graph the function. The coefficient of. Example 1-1a. Example:. First, find the amplitude. Next, find the period. Example 1-1b. Use the amplitude and period to graph the function.

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14.1

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  1. 14.1 Trig. Graphs

  2. Find the amplitude and period for .Then graph the function. The coefficient of Example 1-1a Example: First, find the amplitude. Next, find the period.

  3. Example 1-1b Use the amplitude and period to graph the function. Answer: amplitude: 1; period: 1080 or 6

  4. Find the amplitude and period for .Then graph the function. Amplitude: Period: Example 1-1c Example:

  5. Answer: amplitude: period: 360 or 2 Example 1-1d

  6. Find the amplitude and period for .Then graph the function. Amplitude: Period: Example 1-1e Example:

  7. Example 1-1f Answer: amplitude: 2; period: 1440 or 8

  8. Find the amplitude and period for each function.Then graph the function.a. Answer: amplitude: 1; period: 720 or 4 Example 1-1g Lets do some more:

  9. b. Answer: amplitude: period: 360 or 2 Example 1-1h

  10. c. Answer: amplitude: 3; period: 720 or 4 Example 1-1i

  11. State the amplitude, period, and phase shift for . Then graph the function. Example 2-1a Example: Since a = 2 and b = 1, the amplitude and period of the function are the same as y = 2 cos . However h = –20, so the phase shift is –20. Because h < 0, the parent graphis shifted to the left. To graph y = 2 sin ( + 20), consider the graph of y = 2 sin . Graph this function and then shift the graph 20 to the left.

  12. Answer: amplitude: 2; period: 360; phase shift: 20 left Example 2-1b

  13. State the amplitude, period, and phase shift for Then graph the function. Amplitude: Period: Phase shift: Example 2-1c Example:

  14. Answer: amplitude: period: 2; phase shift: right Example 2-1d The phase shift is to the right, since h > 0.

  15. State the amplitude, period, and phase shift for each function. Then graph the function. a. Answer: amplitude: 3; period: 360; phase shift: –30 Example 2-1e Example:

  16. b. Answer: amplitude: period: 2; phase shift: Example 2-1f

  17. State the vertical shift, equation of the midline, amplitude, and period for . Then graph the function. Since and the vertical shift is –1. Draw the midline, y = –1. The amplitude is 2 and the period is 2. Example 2-2a Example: Draw the graph of the function relative to the midline. Answer: vertical shift: –1; midline: y = –1; amplitude: 2; period: 2

  18. State the vertical shift, equation of the midline, amplitude, and period for . Then graph the function. Amplitude: Period: Example 2-2b Example: Vertical shift: k = 3, so the midline is the graph of y = 3.

  19. Since the amplitude of the function is draw dashed lines parallel to the midline that are unit above and below the midline. Answer:vertical shift: +3; midline: y = 3; amplitude:period: 2 Example 2-2c Then draw the cosine curve.

  20. State the vertical shift, equation of the midline, amplitude, and period for each function. Then graph the function. a. Answer:vertical shift: –2; midline: y = –2; amplitude: 3;period: 2 Example 2-2d Example:

  21. State the vertical shift, equation of the midline, amplitude, and period for each function. Then graph the function. b. Answer:vertical shift: 2; midline: y = 2; amplitude: 3;period: 2 Example 2-2e Example:

  22. State the vertical shift, amplitude, period, and phase shift of Then graph the function. The function is written in the form Identify the values of k, a, b, and h. so the vertical shift is 4. so the amplitude is or 3. so the period is so the phase shift is right. Example 2-3a Example:

  23. Example 2-3b Graph the function. Step 1 The vertical shift is 4. Graph the midline y = 4.

  24. Example 2-3c Step 2 The amplitude is 3. Draw dashed lines 3 units above and below the midline at y = 1 and y = 7.

  25. Step 3 The period is , so the graph is compressed. Graph using themidline as areference. Example 2-3d

  26. Step 4 Shift the graph to the right. Example 2-3e

  27. State the vertical shift, amplitude, period, and phase shift of Then graph the function. Answer: vertical shift: –2; amplitude: 2; period:phase shift: Example 2-3g Example:

  28. Answer: Example 2-3h

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