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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.4 - Solution

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For a number b,b, the graph of y=xby=|x-b| represents a horizontal translation by bb units. If b>0,b>0, the translation is performed to the right. Otherwise, it is performed to the left. Let's rewrite the given absolute value function to match this format. y=x+2y=x(-2)\begin{gathered} y=|x+2| \quad \Leftrightarrow \quad y=|x-({\color{#FF0000}{\text{-} 2}})| \end{gathered} In our equation we have that b=-2.b={\color{#FF0000}{\text{-} 2}}. Therefore, we have to translate the graph of the parent function, y=x,y=|x|, left 22 units.