g(x)=|x + 2|+4\nwe can think of g as a translated (shifted) version of f.\ncomplete the description of the…

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

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

Answer

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.