Given the original function $f(x) = |4x + 3| + 2$, we need to define a new function $g(x)$ that is a translation of $f(x)$ 2 units down. This means subtracting 2 from the function.

The new function $g(x)$ will be:

$g(x) = f(x) - 2$

Substitute $f(x) = |4x + 3| + 2$ into this equation:

$g(x) = (|4x + 3| + 2) - 2$

Simplifying this:

$g(x) = |4x + 3|$

Thus, the function $g(x)$ after translating $f(x)$ 2 units down is:

$g(x) = |4x + 3|$

Would you like a detailed breakdown of how translations affect functions or have any further questions?

Here are 5 questions related to function transformations:

1. How do you translate a function horizontally?
2. What happens when you translate a function 3 units up?
3. Can you describe the effect of translating a function left or right?
4. How does the absolute value in $f(x) = |4x + 3|$ affect its graph?
5. What are other ways to transform functions besides translation?

Tip: A vertical translation shifts a function up or down without altering its shape.