Answer:
y = 2·sin(πx/4) +2
Step-by-step explanation:
You want the equation of the sine function shown in the graph.
Sine function
The graph of the trig function crosses its midline (halfway between the extremes) on the y-axis. This tells you it can be represented by a sine function that has been scaled and shifted vertically.
The equation will be of the form ...
y = A·sin(2πx/P) +B
where A is half the distance between the extremes, B is the vertical position of the midline, and P is the period of the function.
Amplitude
The amplitude A is half the distance between extremes, so is ...
A = (4 -0)/2 = 2
Offset
The vertical translation B is halfway between the extremes, so is ...
B = (4 +0)/2 = 2
Period
The period P is the horizontal distance between points where the function repeats itself. You can look at the x-values of the maxima, minima, or midline crossings to determine P.
Here, the graph crosses the midline at x=0 and x=8, so the period is ...
P = (8 -0) = 8
Equation
Now that we know the parameters, we can write the equation:
[tex]y=2\sin\left(\dfrac{2\pi x}{8}\right)+2\\\\\\\boxed{y=2\sin\left(\dfrac{\vphantom{B}\pi x}{4}\right)+2}[/tex]
