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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.5 - Solution

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

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

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