Question

Given the equation y = 4sin(7(x - 5)) + 3

Answer 1

We are given the following sine function:

`y=4\sin(7(x-5))+3`

This is a function of the form:

`y=A\sin(k(x-a))+b`

Where:

`A=\text{ amplitude}`

Therefore, the amplitude of the given function is 4.

The period of the function is given by:

`T=(2\pi)/(k)`

the value of "k" in the given function is 7, therefore, the period is:

`T=(2\pi)/(7)`

The horizontal shift is given by the value of "a". Since in the given function the value of "a" is 5 this means that the graph is shifted horizontally by 5 units to the right.

The midline is the value of "y" where the graph is divided into two equal parts. It is given by the value of "b". Therefore, the midpoint in the given graph is:

`\begin{gathered} y=3 \\ \\ \end{gathered}`