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Investigation 9: Transformations & Focus D: Graphing Using Transformations

Example

Graph using a mapping rule and a table of values for transformations of the function .

Solution

As the text book points out, state the transformations that has occurred for from this write a mapping rule and then create a new table of values from the basic table of values for .

  • Negative exponent represents a reflection in the y-axis

  • Vertical translation VT = 3

  • Horizontal Translation  HT = -1

  • Mapping Rule

Table of Values:

x

y

-3

-2

-1

0

1

1

2

2

4

3

8

x

y

2

1

0

-1

4

-2

5

-3

7

-4

11

Note the new table is easiest found by using the mapping rule. For example to find the image point for use the mapping rule as follows:

Graph each function: (Note the curve in red is ,which need not be drawn, and the one in black is )

This graph may also be obtained by using the transformations as follows: