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Write an equation with a vertical translation 2 units down from the equation y = -2/9 | x | -7

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A vertical translation of a function f(x) is:


g(x)=f(x)+k

If k is a positive number, the translation is done upward and if it's negative, then it's done downward.

So, if our function is


y=f(x)=-(2)/(9)\mleft|x\mright|-7

And we want to translate it vertically 2 units down, we have to substract 2 from the parent function f(x). Let g(x) be the translated function:


\begin{gathered} g(x)=f(x)-2 \\ g(x)=-(2)/(9)\mleft|x\mright|-7-2 \\ g(x)=-(2)/(9)|x|-9 \end{gathered}

The last one I wrote is the translated function.

User BgRva
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