**Periodic function:**

A periodic function must have the characteristic of where is the period.

**Horizontal shift of a function:**

The graph of is the graph of shifted horizontally by a units.

**Vertical stretching of a function:**

The graph of is the graph of stretched vertically by a units.

** ****Horizontal shrinking of a function:**

The graph of is the graph of shrunk horizontally by a units..

** ****Reflection and vertical shift of a function: **

The graph of is the reflection of the graph about x-axis.

The graph of is the graph of shifted vertically by a units.

**Sinusoidal functions:**

Functions whose equations satisfy .

** ****Amplitude:**

Amplitude is a nonnegative scalar measure of the magnitude of sinusoidal functions.

** ****Period:** For a sinusoidal function the absolute value of is the period of the sinusoidal function.

Phase shift of a sinusoidal function:

For a sinusoidal function the value of is the phase shift of the sinusoidal function.