Presentation is loading. Please wait.

Presentation is loading. Please wait.

Section 1.6 Transformation of Functions

Similar presentations


Presentation on theme: "Section 1.6 Transformation of Functions"— Presentation transcript:

1 Section 1.6 Transformation of Functions

2 Graphs of Common Functions

3

4

5

6 Reciprocal Function

7 Vertical Shifts

8

9 Vertical Shifts

10

11 Example Use the graph of f(x)=|x| to obtain g(x)=|x|-2

12 Horizontal Shifts

13

14 Horizontal Shifts

15 Example Use the graph of f(x)=x2 to obtain g(x)=(x+1)2

16 Combining Horizontal and Vertical Shifts

17 Example Use the graph of f(x)=x2 to obtain g(x)=(x+1)2+2

18 Reflections of Graphs

19

20 Reflections about the x-axis

21

22 Example Use the graph of f(x)=x3 to obtain the graph of g(x)= (-x)3.

23 Example

24 Vertical Stretching and Shrinking

25

26 Vertically Shrinking

27 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.

28 Example Use the graph of f(x)=|x| to graph g(x)= 2|x|

29 Horizontal Stretching and Shrinking

30

31 Horizontal Shrinking

32 Horizontal Stretching

33 Example

34 Sequences of Transformations

35 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

36 Summary of Transformations

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

38 Example

39 Example

40 Example

41 (a) (b) (c) (d)

42 g(x) Write the equation of the given graph g(x). The original function was f(x) =x2 (a) (b) (c) (d)

43 g(x) Write the equation of the given graph g(x). The original function was f(x) =|x| (a) (b) (c) (d)


Download ppt "Section 1.6 Transformation of Functions"

Similar presentations


Ads by Google