Function - 2

Meeting 3

Definition of Composition of Functions

Arrow Diagram of Composition Functions

Examples

Definition of One-to-One Function

Examples

Definition of Inverse of a Function

Example

Example

Exercise

Transformation of Functions

• Shifting• Reflecting• Stretching

Vertical Shifting

Adding a constant to a function shifts its graph vertically; upward if the constant is positive and downward if it is negative.

Horizontal Shifting

The graph of y = f(x - c) is just the graph of y = f(x) shifted to the right c units.Similarly, the graph of y = f(x + c) is just the graph of y = f(x) shifted to the left c units.

Example

Exercise

Reflecting Graphs

Example

Vertical Stretching and Shrinking

Example

Combining Shifting, Stretching,and Reflecting

Horizontal Stretching and Shrinking

Exercise