Given the graph of a function, graph its transformation under translations, reflections, stretchings, and shrinkings.
Transformations of Functions
The graphs of some basic functions are shown on the following page. Others can be seen on the inside back cover.
These functions can be considered building blocks for many other functions. We can create graphs of new functions by shifting them horizontally or vertically, stretching or shrinking them, and reflecting them across an axis. We now consider these transformations.
Vertical Translations and Horizontal Translations
Suppose that we have a function given by
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