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Explanation |
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Objectives
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In order to draw transformation graphs accurately,
you will need to follow some basic rules.
These rules ensure that your final picture will retain the original graph's fundamental shape. The basic idea is to keep track of each transformation separately by monitoring the coordinates of points that reveal the fundamental shape. We can summarize these rules as follows: Rule 1: "Changes Inside" change x-coordinates only. Rule 2: "Changes Outside" change y-coordinates only. Rule 3: We "work from inside to outside."What do we mean by "inside" and "outside ?" Remember that function notation "y = f(x)" corresponds to the actual points on the graph of the function. In particular, inputs are x-coordinates and outputs are y-coordinates. Let's consider the following example. Start with the basic function f(x) = x2. Now consider the "transformed function" g(x) = (x + 3)2 - 1.The " + 3" is "inside" the basic square function, and the " - 1 " is "outside" the basic square function. So we'll use
the " + 3" to change the x-coordinates and the " - 1" to change the y-coordinates of each point on the original Basic Graph |