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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.12 - Solution

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We are asked to graph the equation according to the given transformation. When translating absolute value functions, horizontal translations occur before the absolute value has been evaluated. This is why they are inside the absolute value symbols. Consider the following general equation, where is a real number. The graph of this equation is a horizontal translation of by units. Let's start with the graph of

In this case, is equal to Since we are subtracting a positive value, the transformation will move the graph of to the right by As an example, we will translate three points on the line to the right by units.

Translating each and every point units right means shifting the entire graph of to the right by units.