Learning Resources

Graphing using Transformations

To sketch a graph from the transformational form of

We find the image by analyzing the reflection, stretches and the translations involved.

1. If a is negative, then the original graph is reflected in the x-axis

2. A vertical stretch is determined by the reciprocal of a. The vertical stretch is

3. A vertical translation of q and a horizontal translation of p.

To create a mapping from this form we use

1. Reflection:                              

2. Vertical stretch of              

3. Vertical translation of q         

4. Horizontal translation of p     

If we combine these, the mapping to describe the above transformational equation is