Originally Posted by

**Prove It** OK, if the function is a cos graph, it's of the form

$\displaystyle y = a \cos(bx) + c$,

Where $\displaystyle {\color{red}|}a{\color{red}|}$ is the amplitude, $\displaystyle {\color{red}|}b{\color{red}|} = \frac{2\pi}{Period}$ and $\displaystyle c$ is the mean value.

So $\displaystyle a = 2, b = 2\pi, c = -3$

Which means the function is

$\displaystyle y = 2 \cos (2\pi x) -3$.

Do you see that $\displaystyle g(x)$ is contained in that graph?

So we can write the graph in terms of $\displaystyle g(x)$.

$\displaystyle y = 2g(x) - 3$.