Question

f(x) = |x|
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 blank units and
to the right/left by blank units.

Explanation:

Step1: Analyze vertical shift

For a function \( y = f(x)+k \), if \( k>0 \), it's a shift up by \( k \) units. Here \( g(x)=|x + 2|+4=f(x + 2)+4 \), so vertical shift: up by 4 units.

Step2: Analyze horizontal shift

For a function \( y = f(x + h) \), if \( h>0 \), it's a shift left by \( h \) units. Here \( g(x)=f(x + 2)+4 \), so horizontal shift: left by 2 units.

Answer:

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