Question

f(x) = |x|
g(x) = |x + 9| - 5
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 to the right/left by units.

Explanation:

Step1: Identify horizontal shift rule

For $f(x-h)$, shift $f(x)$ right $h$ units; for $f(x+h)$, shift left $h$ units. Here, $g(x)$ has $|x+9|=|x-(-9)|$, so $h=-9$.

Step2: Identify vertical shift rule

For $f(x)+k$, shift $f(x)$ up $k$ units; for $f(x)-k$, shift down $k$ units. Here, $g(x)$ has $|x+9|-5$, so $k=-5$.

Step3: Match shifts to blanks

Horizontal shift: left by 9 units. Vertical shift: down by 5 units.

Answer:

To get the function $g$, shift $f$ down by $\boldsymbol{5}$ units and to the left by $\boldsymbol{9}$ units.