Question

Select the correct graph and function.

Answer 1

The answer is: $g(t)=4sin(\frac{\pi}{6}x)$ and the graph is shown in the image attached.

The explanation for this problem is shown below:

1. You have that the high tide was about $4ft$ above average sea level, and the low tide was about $4ft$ below average sea level. So, the amplitude of the function must be $4$:

2. The formula for calculate the amplitude from a graph is:

$A=\frac{maximum-minimum}{y2}$

3. As you can see in the graph attached, the maximum is $4$ and the minimum is $-4$. Then, the amplitude is:

$A=\frac{4-(-4)}{2}=4$

4. The amplitude of the sine function is the absolute value of $a$ in $y=asin(bx+c)+d$. Therefore the amplitude of the function mentioned is: $a=4$ and the period is $P=\frac{2\pi}{\frac{\pi}{6}} =12$, which corresponds with the period shown in the graph (the repeating of the pattern of the wave).