Question

I need help with this practice I am having a tough time solving it properly

Answer 1

Given:

There are given that the parent functions as a cosine function:

Where,

The amplitude of the function is 9.

The vertical shift is 11 units down.

Explanation:

To find the cosine function, we need to see the standard form of the cosine function:

$f(x)=acos(bx+c)+d$

Where,

a is the amplitude of the function,

Now,

According to the question:

The amplitude of the function is 9, which means:

$f(x)=9cos(bx+c)+d$

The vertical shift is 11 units down, which means:

$f(x)=9cos(bx+c)-11$

For period:

$\begin{gathered} f(x)=-9cos(\frac{12\pi}{7}x+0)-11 \\ f(x)=-9cos(\frac{12\pi}{7}x)-11 \end{gathered}$

Final answer:

Hence, the cosine function is shown below;

$f(x)=-9cos(\frac{12\pi}{7}x)-11$