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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.15 - Solution

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We are asked to translate the graph of y=xy=|x| down 55 units. Recall that, when translating absolute value functions, vertical translations occur outside the absolute value symbol. Let's consider a general equation, where a{\color{#0000FF}{a}} is a real number. y=x+a\begin{aligned} y=|x|+{\color{#0000FF}{a}} \end{aligned} The graph of the above equation is a vertical translation up a{\color{#0000FF}{a}} units of the graph of y=x.y=|x|. In our case, since the translation is performed down, the value of a{\color{#0000FF}{a}} is -5.{\color{#0000FF}{\text{-} 5}}. y=x5\begin{aligned} y = |x|-5 \end{aligned}