Chapter 6, Problem 10CR

Graph $y=3\sin \left(2x\right)$.

To determine

To graph: The equation $y=3\sin \left(2x\right)$

Explanation of Solution

Given information:

The equation is $y=3\sin \left(2x\right)$

Graph:

To get the graph of $y=3\sin \left(2x\right)$, perform the transformations as follows:

Step 1: Begin with the graph of the base function $y=\sin x$.

Step 2: Horizontally, compress the graph by $\frac{1}{2}$ units gives $y=\sin \left(2x\right)$

Step 3: Vertically, stretch the graph by factor $3$ units gives $y=3\sin \left(2x\right)$

From the above graph,

The domain of the function is $\left(-\infty ,\infty \right)$ and the range of the function is $\left[-3,3\right]$

Interpretation:

The graph represents function of $y=3\sin \left(2x\right)$