Basic functions: Power functions
Transformations of power functions
Transformation of a power function By horizontal and vertical translation, and by vertical multiplication of the graph of the power function the graph of the function
can be created. For an arbitrary fractional linear function can be constructed and for an arbitrary quadratic function can be constructed in this way.
To illustrate transformations of power functions, we consider the horizontal and vertical translation as well as the vertical scaling of the graph of the power function .
Vertical translation
We translate the graph of vertically over a distance .
The new function becomes
The point of symmetry of is , i.e., the graph of does not change when reflected in .
Horizontal translation
We translate the graph of horizontally over a distance .
The new function becomes
The point of symmetry of is , i.e., the graph of does not change when reflected in .
Vertical scaling
We scale the graph of vertically by .
The new function becomes
The symmetry point of the power function remains in place.
If , then the graph of is the mirror image of the graph of in the horizontal axis, but also in the vertical axis.
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