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

Question

asked Sep 18, 2023 228k views

1 Answer

BgRva · Answer 1 · 2023-09-23T04:50:16+0000

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

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.