Composite Transformations
Key points
- Composite transformations are when a graph undergoes multiple consecutive transformations.
- Vertical and horizontal stretches/compressions come before translations.
Composite transformations, also known as sequence transformations, are when a graph is transformed multiple times, with different transformations.
- One transformation produces an image upon which the next transformation is then performed.
- In the example, the red graph is the result of the black graph undergoing a vertical stretch, then a vertical translation.
With composite transformations, order matters.
- A different order yields a different result.
- Vertical and horizontal stretches/compressions comes first.
- Reflections over the x and y axis come next.
- Translations are the last step.
- Reflections over the x and y axis come next.
Summary of Graph Transformations:
- Vertical and horizontal translations include adding or subtracting a constant from either the x or y values.
- Reflections over the x or y axis consist of multiplying the x or y values by -1.
- Vertical and horizontal stretches consist of multiplying x or y values by a constant.
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