1. Section 1.6 Transformation of Functions

2. Graphs of Common Functions

7. Vertical Shifts

9. Vertical Shifts

11. Horizontal Shifts

13. Reflections of Graphs

16. Example

17. Vertical Stretching and Shrinking

19. Vertically Shrinking

20. Vertically Stretching
Graph of f(x)=x3
Graph of g(x)=3x3
This is vertical stretching – each y coordinate is multiplied by 3 to stretch the graph.

21. Sequences of Transformations

22. A function involving more than one transformation can be graphed by performing transformations in the following order:
Horizontal shifting
Stretching or shrinking
Reflecting
Vertical shifting

23. Summary of Transformations

24. A Sequence of Transformations
Starting graph.
Move the graph to the left 3 units
Stretch the graph vertically by 2.
Shift down 1 unit.

25. Example

26. Example

27. Example