The sinusoidal function that is modeled in the graph presented in this question is the expression y = 5 + 3 · sin [π · (x+2)/4], where x and y are the independent and dependent variable, respectively.
How to model a sinusoidal function
In this question we must analyze periodic functions to determine the most appropriate model that best fit with the graph, the determination of the model will determine the inherent characteristics of the model. The graph seem to be a sinusoidal function.
Sinusoidal functions are bounded functions characterized by use of trigonometric expressions and the presence a lower and a upper bound, a period and phase. The entire formula is described below:
y = r + 0.5*(M-m) · sin [2π · (x-F)/T] (1)
Where:
- r - Middle value
- m - Lower bound
- M - Upper bound
- F - Phase
- x - Independent value
- y - Dependent value
- T - Period
The period is the time in which a sinusoidal function completes a cycle and the phase is a horizontal translation applied to a canonical sinusoidal function.
If we know that r = 5, m = 2, M = 8, T = 8 and F = -2, then the sinusoidal function is:
y = 5 + 3 · sin [π · (x+2)/4]
The sinusoidal function that is modeled in the graph presented in this question is the expression y = 5 + 3 · sin [π · (x+2)/4], where x and y are the independent and dependent variable, respectively. [tex]\blacksquare[/tex]
To learn more on sinusoidal function, we kindly invite to check this verified question: https://brainly.com/question/12060967
