Write a function g, f(x) = l4x+3l + 2; g is a translation 2 units down

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.

Write a function g, f(x) = |4x+3| + 2; g is a translation 2 units down.

Learn how to translate the absolute value function f(x) = |4x + 3| + 2 by two units down to get g(x) = |4x + 3|. This problem covers function transformations and is suitable for students in Grades 9-12.

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