Final Answer:
a. The period of the function is 2 units.
b. The minimum value of this function is -3.5.
c. The maximum value of this function is 3.54.
d. The midline of this function is y = 0.
e. The amplitude of this function is 3.54.
f. The function representing the behavior of the graphed function is g(a) = 1.77 * sin(π * a).
Step-by-step explanation:
a. The period of a periodic function is the horizontal length of one complete cycle of the graph. Looking at the given graph, it repeats after a horizontal span of 2 units, so the period of this function is 2 units.
b. To find the minimum value of the function, observe the lowest point on the graph, which corresponds to -3.5 on the y-axis. Thus, the minimum value of this function is -3.5.
c. Similarly, the highest point on the graph corresponds to 3.54 on the y-axis, indicating the maximum value of this function as 3.54.
d. The midline of a periodic function is the horizontal line that divides the graph symmetrically. From the graph, it's evident that the function oscillates equally above and below y = 0; hence, the midline of this function is y = 0.
e. The amplitude of a periodic function is half the vertical distance between the maximum and minimum values. Here, it's (3.54 - (-3.5)) / 2 = 1.77, so the amplitude of this function is 1.77.
f. The behavior of the graphed function resembles a sine function with an amplitude of 1.77 and a period of 2 units. The general equation for such a function is g(a) = A * sin(Bπ * a), where A is the amplitude and B is determined by the period. Therefore, the function representing this behavior is g(a) = 1.77 * sin(π * a).