Answer
See graph.
domain $(-\infty,\infty)$, range $[-2,2]$
Work Step by Step
Step 1. To graph $y=2sin(4x)$, start from one period of $sin(x)$, shrink horizontally by a factor of $1/4$, then stretch vertically by a factor of 2. Repeat the resulting curve horizontally to cover more regions. See graph.
Step 2. We can determine the domain $(-\infty,\infty)$, range $[-2,2]$
