Transformations of Periodic Functions

Sketch the graph of the following, indicating the amplitude and period, and showing at least two cycles:

$y=\sin (-x)$

Sketch the graph of the following, indicating the amplitude and period, and showing at least two cycles:

$y=\sin x+12$

This graph is a result of a transformation on $y=\sin x$ or $y=\cos x$

Identify the transformation, and determine the function of the transformed graph.

State the amplitude, frequency, and period of each graph. Sketch the graph for $-360°\le x\le 360°$

$y=3\cos 0.5x-1$

State the amplitude, frequency, and period of each graph. Sketch the graph for $-360°\le x\le 360°$

$y=0.5\sin 2x+3$

State the amplitude, frequency, and period of each graph. Sketch the graph for $-360°\le x\le 360°$

$y=-\sin \left(0.5x\right)$

State the amplitude, frequency, and period of the given graph. Sketch the graph for $-360°\le x\le 360°$

$y=4\cos 3x$

Draw the graph of the function $y=\frac{5}{2}\sin \left(\frac{-x}{3}\right)$ showing at least two cycles. Be sure to clearly indicate the amplitude and period.

Draw the graph of the function $y=\frac{2}{3}\cos 8x$ showing at least two cycles. Be sure to clearly indicate the amplitude and period.

Draw the graph of the function $y=7\cos 5x$ showing at least two cycles. Be sure to clearly indicate the amplitude and period.

Draw the graph of the function $y=0.4\sin \left(2x\right)$ showing at least two cycles. Be sure to clearly indicate the amplitude and period.

For the following graph, find the amplitude, frequency, and period. Then, write down the equation that represents the function.

For the following graph, find the amplitude, frequency and period. Then, write down the equation that represents the function.

Determine which two transformations transform $y=\sin x$ to $y=3\sin 2x$.

The following graph is a result of a combination of transformations on $y=\sin x$ or $y=\cos x$. 

Identify the transformations, and determine the function of the transformed graph.

The following graph is a result of a combination of transformations on $y=\sin x$ or $y=\cos x$. 

Identify the transformations, and determine the function of the transformed graph.

The following graph is a result of a combination of transformations on $y=\sin x$ or $y=\cos x$. 

Identify the transformations, and determine the function of the transformed graph.

Describe in words how to transform the graph of $y=\sin x$ to $y=\frac{3}{4}\sin \left(\frac{3x}{4}\right)$.

Describe in words how to transform the graph of $y=\sin x$ to $y=-3\sin 3x+3$.

Describe in words how to transform the graph of $y=\sin x$ to $y=\frac{1}{2}\sin \left(\frac{x}{3}\right)-4$.