Question

Really need help solving this practice from my ACT prep guide It’s a trig practice

Answer 1

Given:

- The amplitude of the Sine Function:

`A=10`

- The midline:

`y=4`

- And the period:

`Period=2`

- You know that the function does not have a Phase shift.

• You need to remember that, by definition, the General Equation for a Sine Function has this form:

`y=Asin\mleft(B\mleft(x+C\mright)\mright)+D`

Where "A" is the amplitude, "C" is the phase shift, "D" is the vertical shift and this is the period:

`Period=(2\pi)/(B)`

Since the midline is given by the vertical shift, you can identify that, in this case:

`D=4`

And, knowing the period, you can set up that:

`2=(2\pi)/(B)`

Solving for "B", you get:

`\begin{gathered} 2B=2\pi \\ \\ B=(2\pi)/(2) \\ \\ B=\pi \end{gathered}`

• It is important to remember the following Transformation Rule for Functions:

When:

`-f(x)`

The function is reflected over the x-axis.

Therefore, knowing all the data, you can set up this equation:

`f(x)=-10\sin (\pi x)+4`

Hence, the answer is: First option.