Question

f(x) = |x|
g(x) = |x - 4| - 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 to the right/left by □ units.

Explanation:

Step1: Analyze horizontal shift

For a function \( y = f(x - h) \), the graph shifts \( h \) units to the right if \( h>0 \), and \( h \) units to the left if \( h<0 \). Here, \( f(x)=|x| \) and \( g(x)=|x - 4|-4 \). The horizontal part is \( x-4 \), so \( h = 4>0 \), meaning a shift to the right by 4 units.

Step2: Analyze vertical shift

For a function \( y = f(x)+k \), the graph shifts \( k \) units up if \( k>0 \), and \( k \) units down if \( k<0 \). Here, the vertical part is \( - 4 \), so \( k=-4<0 \), meaning a shift down by 4 units.

Answer:

To get the function \( g \), shift \( f \) up/down by \( 4 \) units (down) and to the right/left by \( 4 \) units (right). So the blanks are: down, 4, right, 4.