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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.3 - Solution

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We are asked to graph the equation y=xy=|x| 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 h{\color{#0000FF}{h}} is a real number. y=xh\begin{aligned} y=|x-{\color{#0000FF}{h}}| \end{aligned} The graph of this equation is a horizontal translation of y=xy=|x| by h{\color{#0000FF}{h}} units. Let's start with the graph of y=x.y=|x|.

In this case, h{\color{#0000FF}{h}} is equal to 2.5{\color{#0000FF}{2.5}} since it's a translation to the right. To do this, we will translate three points on the line y=xy=|x| to the right by 2.5{\color{#0000FF}{2.5}} units.

Translating each and every point 2.52.5 units right means shifting the entire graph of y=xy=|x| to the right by 2.52.5 units.