4. Shifting, Reflecting, and Stretching Graphs
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Rigid transformations can only change the position of the graph of a function in the coordinate plane.
Horizontal shifts, vertical shifts, reflections
We want to name three types of rigid transformations. First, recall that rigid transformations can only change the position of the graph of a function in the coordinate plane. The basic shape of the graph remains unchanged. Horizontal shifts, vertical shifts, and reflections are examples to this type of transformations.
| Rigid Transformations of the Graph of f(x) | |
|---|---|
| Vertical Shifts | Vertical shift k units upward, k>0 y=f(x)+k |
| Vertical shift k units downward, k>0 y=f(x)-k | |
| Horizontal Shifts | Horizontal shift h units to the right, h>0 y=f(x-h) |
| Horizontal shift h units to the left, h>0 y=f(x+h) | |
| Reflections | Reflection in the x-axis y=- f(x) |
| Reflection in the y-axis y=f(- x) | |