Question

g(x)=|x + 2|+4
we can think of g as a translated (shifted) version of f.
complete the description of the transformation.
use nonnegative numbers.
to get the function g, shift f up/down by units and the right/left by units.

Explanation:

Step1: Recall the transformation rules for absolute - value functions

The general form of an absolute - value function is \(y = |x - h|+k\), where \((h,k)\) represents the translation. If \(h>0\), the graph is shifted to the right by \(h\) units; if \(h < 0\), the graph is shifted to the left by \(|h|\) units. If \(k>0\), the graph is shifted up by \(k\) units; if \(k < 0\), the graph is shifted down by \(|k|\) units.
The parent function \(f(x)=|x|\) and the function \(g(x)=|x + 2|+4=|x-(-2)|+4\)

Step2: Determine the horizontal and vertical shifts

For the horizontal shift:
We have \(h=-2\) in the formula \(y = |x - h|+k\). Since \(h=-2\), the graph of \(y = |x|\) is shifted to the left by \(| - 2|=2\) units.
For the vertical shift:
We have \(k = 4\) in the formula \(y=|x - h|+k\). Since \(k = 4>0\), the graph of \(y = |x|\) is shifted up by \(4\) units.

Answer:

To get the function \(g\), shift \(f\) up by \(4\) units and to the left by \(2\) units.