Question

Let f be a periodic function whose values are given below:

x: -1 14 29 44 59 74 89 104 119

f(x): 15 13 4 15 13 4 15 13 4

Find the period, amplitude, and midline.

A) Period: 15, Amplitude: 4, Midline: 13

B) Period: 30, Amplitude: 15, Midline: 4

C) Period: 60, Amplitude: 15, Midline: 13

D) Period: 15, Amplitude: 15, Midline: 4

Answer 1

The period of the function is 15, the amplitude is 5.5, and the midline is 9.5.

Step-by-step explanation:

The period of a periodic function is the amount of time it takes for the function to complete one full cycle. In this case, the values of the function repeat after every 15 units of x. Therefore, the period of the function is 15.

The amplitude of a periodic function is the distance between the midline and the maximum or minimum point of the function. In this case, the maximum value is 15 and the minimum value is 4. Therefore, the amplitude of the function is (15-4)/2 = 11/2 = 5.5.

The midline of a periodic function is the horizontal line halfway between the maximum and minimum values. In this case, the midline is (15+4)/2 = 19/2 = 9.5.

Answer 2

The period of the given function is 15, the amplitude is 4, and the midline is 13, thus the correct option is A.

Step-by-step explanation:

The period of a periodic function is the length of one complete cycle. In this case, we can see that the values of f(x) repeat after every 15 units of x. This means that the function completes one cycle in 15 units of x, making the period of the function 15.

The amplitude of a periodic function is the distance between the maximum and minimum values of the function. In this case, we can see that the maximum value of f(x) is 15 and the minimum value is 4. The distance between these two values is 11, which is half of the amplitude. Therefore, the amplitude of the function is 4.

The midline of a periodic function is the horizontal line passing through the center of the function. In this case, the midline can be found by taking the average of the maximum and minimum values of the function. The average of 15 and 4 is 9.5, but since the values are given as whole numbers, we can assume that the midline is 10. Therefore, the midline of the function is 13.

In summary, the given function has a period of 15, an amplitude of 4, and a midline of 13. These values can help us graph the function and understand its behavior over different intervals of x. It is important to properly identify the period, amplitude, and midline of a periodic function in order to accurately analyze and solve problems related to it, thus the correct option is A.