Answer:
Option 1.[tex]f(x) = -3sin(\frac{\pi }{6}x)+3[/tex]
Step-by-step explanation:
The height of the tide over the time is shown on the graph.
Its a periodic function (sine graph) plotted on a graph in which variables are
Amplitude a = (6-0)/2 = 3
Period = 15-3 = 12
Therefore b = 2π/period = 2π/12 = π/6
horizontal shift = 0
Vertical shift = 3
Since the function starts with negative sign that means its below the x-axis.
So as per standard formula of f(x) = asin(bx+c)+d
option which matches all these parameters is Option 1. [tex]f(x) = -3sin(\frac{\pi }{6}x)+3[/tex]
