Question

Let y = f(x) be a periodic function whose values are given below. Find the period, amplitude, and midline.

x 5 7 9 11 13 15 17 19 21
f(x) 18 16 1 18 16 1 18 16 1

The period of the graph is___

Answer 1

The period of the given periodic function is 8 units, the amplitude is 8.5 units, and the midline is y = 9.5.

Step-by-step explanation:

The periodic function given by the values has certain characteristics that can be identified. To find the period of the graph, we look for the value of 'x' at which the function's values begin to repeat. Here, the function repeats its values at x=5 with f(x)=18, and then again at x=13 with f(x)=18, indicating one complete cycle. The period is the difference between these x-values, so the period is 13 - 5 = 8 units.

To determine the amplitude of the function, which is the value from the midline to the peak, we observe that the maximum value is 18 and the minimum is 1. The midline is at the average value between these extremes, which means the midline is at (18 + 1) / 2 = 9.5. The amplitude is then (18 - 9.5) = 8.5 units.

Finally, the midline of the function is the horizontal line that bisects the function. As calculated above, it is the line y = 9.5.