Question

Can someone help me with this

Answer 1

Answer:  Period = 4

               Amplitude = 3

Step-by-step explanation:

Period is the interval of one "cycle" before the pattern repeats.

If you notice that when x = 0, y = -4.  

When does the pattern repeat (reach -4 again)?

Answer: when x = 4.

So the interval of one "cycle" is 4 units -->  Period = 4.

$Amplitude=\dfrac{Max-Min}{2}=\dfrac{2-(-4)}{2}=\dfrac{6}{2}=\bold{\large\boxed{3}}$

Answer 2

Answer:

• amplitude: depends on your definition (see discussion)
• period: 4

Step-by-step explanation:

For the definition of "amplitude" you are to use in this situation, you should refer to your curriculum materials. When the function is symmetrical about its average value, the amplitude is defined as the (positive) maximum difference between the function and its average value.

Here, the average value of this function is 1/2, so the amplitude in the positive direction is 2 -0.5 = 1.5, and in the negative direction, it is 0.5 -(-4) = 4.5. The amplitude of this function could be said to be 4.5.

In some cases, the amplitude is described as half the difference between the maximum and minimum. Here, the maximum is 2 and the minimum is -4, so the difference is 6. Half that would be 3, so the amplitude of this function could be said to be 3.

In other cases where the function shows this kind of asymmetry, the amplitude is considered to be the deviation from a baseline. We could take y=2 to be the baseline, so the amplitude would be 2 -(-4) = 6. The amplitude of this function could be said to be 6.

In short, the amplitude depends on your definition when the function is not symmetrical about a horizontal line.

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The period is the horizontal distance between repetitions of the function values. Here, we can see the negative peaks occur every 4 units. The period is 4 units.

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Comment on average value

The average value is found by integrating the function over one period and dividing that integral by the length of the period. Here it is ...

  $\displaystyle\frac{1}{4}\int^4_0{f(x)} \, dx =\frac{1}{2}$

You can verify this is the case by computing the area above the line y=1/2 and the area below the line y=1/2. You find they are both 27/8.