function - 2 meeting 3. definition of composition of functions
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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
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