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# Describing Transformations of Absolute Value Functions

## Describing Transformations of Absolute Value Functions 1.15 - Solution

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