Question

23–36 ■ Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

\(y = 4sin\left( {3x} \right)\)

Short answer

The plot of the function \(y = 4sin\left( {3x} \right)\) is

Step-by-step solution

Given data

The function to be plotted is

\(y = 4\sin \left( {3x} \right)\)

Plot of the function \(y = sinx\)

The plot of the function \(y = \sin x\) is as follows

Figure 1

Plot of the function \(y = 4sin\left( {3x} \right)\)

The plot of the function \(y = \sin \left( {3x} \right)\) can be obtained by increasing the frequency of the oscillating function in Figure 1 by 3 as follows

Figure 2

The plot of the function \(y = 4\sin \left( {3x} \right)\) can be obtained by increasing the amplitude of the oscillating function in Figure 2 by 4 as follows

Figure 3