Question

Hello please use original message to do the work and to have the final explanation.

Answer 1

we are asked to determine the sine function of the given graph. To do that we will use the general form of the sine function:

$y=A\sin (k(\theta-b))+c$

"A" is the amplitude and is the maximum value of the function in this case the maximum value is 6, therefore, A = 6.

The value of "c" is the upward shift of the graph, in this case, the graph was an upward shift of 3, therefore, c = 3}

The value of "k" can be found from the period using the following formula:

$T=\frac{2\pi}{k}$

The period, in this case, is 4, replacing in the previous equation:

$4=\frac{2\pi}{k}$

Solving for "k":

$k=\frac{\pi}{2}$

The value of "b" is the horizontal shift of the graph, in this case is: