This activity involves operations which change a function by changing its
graph: these operations are called transformations of the graph.
Using transformations, we can start from one function and generate
a family of functions which share some common features.
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The dynamic figures below are meant to give a "feel" for transformations.
In these figures you can translate and strech graphs to get new
graphs. In the first figure, when you point to the graph and
the cursor changes from "arrow" to "hand", you can translate
the graph in various directions.
In the second figure, when you point to the graph and
the cursor changes from "arrow" to "hand", you can strech
the graph horizontally by making horizontal motions with the cursor, or
vertically by making vertical motions.
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The following dynamic figure presents families
of functions which are generated by translations or stretching.
By choosing the type transformation and using the "transform"
button, you can generate different examples of such families.
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| Families generated by transformations |
The tools for this activity, as well as the general
Transformations tool from the tools list, enable you to study the transformations and examine their
effect on various representations of the function: the graphical representation, the
value-table and the correspondence rule.
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Write an essay on transformations
Study the translation, stretching, and reflection transformations.
Among the issues you can examine:
How are each of the transformations
expressed in the various representations of the function:
- The graph
- The correspondence rule
- The table?
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What is the meaning of the numbers
"translation size" and "strech factor"?
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How do the the various transformations affect
the features of a quadratic function, for example
- Symmetry,
- Domains of increase and decrease,
- Intersections with the axes (the number of intersections and their location).
- Vertex.
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What are the common properties of
families of functions formed by performing a certain type of
transformations on a quadratic function?
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