In this packet we will see several of the basic ways in which we can transform one function into another. Starting with a curve on the plane, we will see how the curve can be stretched, compressed, and shifted around both vertically and horizontally.
Transformations are often useful when we are trying to fit one curve to a collection of data - we often almost see a pattern to a collection of data points in the plane, but we don't have exactly the right function to model them. By getting the basic relationship right with a starting function, we can often apply simple transformations to that function until it more accurately models the data in question.
In the following two videos, we see the basics of function transformation.
In this video we see horizontal and vertical translations and we see reflections about the x and y axes.
This video shows horizontal and vertical stretching and compressions of functions.