Answer:
Explanation:
To find a sinusoidal function that matches the given graph, we need to find the amplitude (A), period (T), phase shift (h), and vertical shift (k) of the function.
Since the graph goes through the points (-9,0) and (5,0), we know that the maximum value of the function is located at the average of the x-values, which is -2, and that the minimum value of the function is located at the average of the x-values, which is (9+5)/2 = 7. The amplitude of the function can be found by taking half the difference of the maximum and minimum y-values, which is 0 - (-2)/2 = 1.
The period of the function can be found by taking the difference of the x-values of two consecutive maxima or minima, which is 5-(-9) = 14.
The phase shift can be found by noting the horizontal shift of the graph from its standard form, which is usually given by the equation y = A sin(x). In this case, the graph is shifted 2 units to the right, so the phase shift is 2.
The vertical shift can be found by noting the location of the midline of the graph, which is half way between the maximum and minimum y-values. In this case, the midline is at y = -1.
Putting all these values together, we can write a sinusoidal function that matches the given graph as:
f(x) = 1 sin(x + 2π/14) - 1
This function has amplitude 1, period 14, phase shift 2π/14 to the right, and a vertical shift of -1 down.