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```markdown
Given:
[tex]\[
\begin{array}{l}
f(x) = |x| \\
g(x) = |x+2| + 4
\end{array}
\][/tex]

We can think of [tex]\( g \)[/tex] as a translated (shifted) version of [tex]\( f \)[/tex].
Complete the description of the transformation. Use nonnegative numbers.

To get the function [tex]\( g \)[/tex], shift [tex]\( f \)[/tex] up/down by [tex]\(\square\)[/tex] units and right/left by [tex]\(\square\)[/tex] units.
```

(Note: The previous response had some irrelevant or nonsensical fragments and errors which were removed for clarity.)



Answer :

GinnyAnswer
To describe the transformation of the function [tex]\( f(x) = |x| \)[/tex] to the function [tex]\( g(x) = |x + 2| + 4 \)[/tex], we need to perform the following steps:

1. Shift Left: The term [tex]\( |x + 2| \)[/tex] indicates that the function [tex]\( f(x) = |x| \)[/tex] is shifted to the left by 2 units. This is because adding 2 inside the absolute value function [tex]\( f(x) \)[/tex] translates the graph horizontally in the negative direction.

2. Shift Up: The term [tex]\( + 4 \)[/tex] outside the absolute value function indicates that the entire graph is shifted upward by 4 units. This vertical shift is added to the output of the function [tex]\( |x + 2| \)[/tex].

Therefore, to obtain the function [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex], we do the following transformations:

- Shift [tex]\( f \)[/tex] to the left by 2 units.
- Shift [tex]\( f \)[/tex] up by 4 units.

So, to complete the description in the question:
To get the function [tex]\( g \)[/tex], shift [tex]\( f \)[/tex] up/down 4 units and to the right/left by 2 units.

This perfectly describes the transformation required.

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