Question

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Table 1.2.3, and then applying the appropriate transformations.

15. \(y = - \sqrt x - {\bf{1}}\)

Short answer

The graph of the function \(y = \sin 4x\) is obtained from the graph of \(y = \sin x\) by changing the period to \(\frac{{2\pi }}{4}\) , i.e., \(\frac{\pi }{2}\).

In other words, it can be said that the curve of \(y = \sin x\) is compressed by a factor of 4.

Step-by-step solution

Write the transformation to find the graph of \(y = {\bf{sin4}}x\)

The graph of the function \(y = \sin 4x\) is obtained from the graph of \(y = \sin x\) by changing the period to \(\frac{{2\pi }}{4}\) , i.e., \(\frac{\pi }{2}\).

In other words, it can be said that the curve of \(y = \sin x\) is compressed by a factor of 4.

Sketch the graph of transformation from \(y = {\bf{sin}}x\) to \(y = {\bf{sin4}}x\)

The figure below represents the graph of \(y = \sin x\):

The figure below represents the graph of \(y = \sin 4x\):

Thus, the graph of the function is obtained