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:
[tex]f(x)=acos(bx+c)+d[/tex]
Where,
a is the amplitude of the function,
Now,
According to the question:
The amplitude of the function is 9, which means:
[tex]f(x)=9cos(bx+c)+d[/tex]
The vertical shift is 11 units down, which means:
[tex]f(x)=9cos(bx+c)-11[/tex]
For period:
[tex]\begin{gathered} f(x)=-9cos(\frac{12\pi}{7}x+0)-11 \\ f(x)=-9cos(\frac{12\pi}{7}x)-11 \end{gathered}[/tex]
Final answer:
Hence, the cosine function is shown below;
[tex]f(x)=-9cos(\frac{12\pi}{7}x)-11[/tex]
