Question

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

Answer 1

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

$y=f(x)=-\frac{2}{9}\mleft|x\mright|-7$

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:

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

The last one I wrote is the translated function.