function - 2 meeting 3. definition of composition of functions
TRANSCRIPT
![Page 1: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/1.jpg)
Function - 2
Meeting 3
![Page 2: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/2.jpg)
Definition of Composition of Functions
![Page 3: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/3.jpg)
Arrow Diagram of Composition Functions
![Page 4: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/4.jpg)
Examples
![Page 5: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/5.jpg)
Definition of One-to-One Function
![Page 6: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/6.jpg)
Examples
![Page 7: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/7.jpg)
Definition of Inverse of a Function
![Page 8: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/8.jpg)
![Page 9: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/9.jpg)
![Page 10: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/10.jpg)
Example
![Page 11: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/11.jpg)
Example
![Page 12: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/12.jpg)
![Page 13: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/13.jpg)
Exercise
![Page 14: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/14.jpg)
Transformation of Functions
• Shifting• Reflecting• Stretching
![Page 15: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/15.jpg)
Vertical Shifting
Adding a constant to a function shifts its graph vertically; upward if the constant is positive and downward if it is negative.
![Page 16: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/16.jpg)
![Page 17: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/17.jpg)
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.
![Page 18: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/18.jpg)
Example
![Page 19: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/19.jpg)
Exercise
![Page 20: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/20.jpg)
Reflecting Graphs
![Page 21: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/21.jpg)
Example
![Page 22: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/22.jpg)
Vertical Stretching and Shrinking
![Page 23: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/23.jpg)
Example
![Page 24: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/24.jpg)
Combining Shifting, Stretching,and Reflecting
![Page 25: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/25.jpg)
Horizontal Stretching and Shrinking
![Page 26: Function - 2 Meeting 3. Definition of Composition of Functions](https://reader036.vdocuments.site/reader036/viewer/2022062517/56649f335503460f94c50250/html5/thumbnails/26.jpg)
Exercise