The function $\displaystyle {f}$ is periodic with a period $\displaystyle {p}={3}$. The function $\displaystyle {g}$ is periodic with a period $\displaystyle {q}={4}$. The necessary information for each function is presented below ($\displaystyle {f}$ in table on left and $\displaystyle {g}$ on right).

$\displaystyle {x}$ $\displaystyle {y}={f{{\left({x}\right)}}}$ 0 2 1 -3 2 -3 3 2

$\displaystyle {x}$ $\displaystyle {y}={g{{\left({x}\right)}}}$ 0 2 1 -2 2 -2 3 -2 4 2

We will define a new periodic function $\displaystyle {R}{\left({x}\right)}={f{{\left({x}\right)}}}+{g{{\left({x}\right)}}}$.
Answer the following for the function $\displaystyle {R}{\left({x}\right)}$.
0. Make a graph of $\displaystyle {R}{\left({x}\right)}$ the spans at least two periods (this of course will not be entered into wamap, but you should still do it a few times).
1. What is the period of the function $\displaystyle {R}$?
2. Evaluate $\displaystyle {R}{\left({11.1}\right)}=$
3. Evaluate $\displaystyle {R}{\left({16}\right)}=$
4. Evaluate $\displaystyle {R}{\left({55.8}\right)}=$
5. Evaluate $\displaystyle {R}{\left({806}\right)}=$