Answer
$$\eqalign{
& {\text{amplitude: 2}} \cr
& {\text{period: }}8\pi \cr
& {\text{vertical translation}}:1{\text{ up}} \cr
& {\text{phase shift}}:{\text{none}} \cr} $$
Work Step by Step
$$\eqalign{
& y = 1 + 2\sin \frac{1}{4}x \cr
& {\text{Rewrite the function}} \cr
& y = 2\left[ {\sin \frac{1}{4}\left( {4x - 0} \right)} \right] + \frac{1}{2} \cr
& {\text{The function is written in the form }}y = a\sin \left[ {b\left( {x - d} \right)} \right] + c \cr
& \underbrace {y = 2\left[ {\sin \frac{1}{4}\left( {4x - 0} \right)} \right] + \frac{1}{2}}_{y = a\sin \left[ {b\left( {x - d} \right)} \right] + c} \cr
& {\text{with:}} \cr
& a = 2,\,\,\,b = \frac{1}{4},\,\,\,\,d = 0,{\text{ }}c = 1 \cr
& \cr
& {\text{The amplitude is given by }}\left| a \right|,\,\,\,\,\left| a \right| = \left| 2 \right| = 2 \cr
& {\text{The period is given by }}\frac{{2\pi }}{b} = \frac{{2\pi }}{{1/4}} = 8\pi \cr
& {\text{The vertical translation is }}c = 1\,{\text{up}} \cr
& {\text{The phase shift is }}d{\text{ translation is }}d = 0,{\text{ none}} \cr
& \cr
& {\text{amplitude: 2}} \cr
& {\text{period: }}8\pi \cr
& {\text{vertical translation}}:1{\text{ up}} \cr
& {\text{phase shift}}:{\text{none}} \cr} $$
