The question in the image asks to find the new function $g(x)$ after translating the function $f(x) = |x|$ left 1 unit and up 2 units.

For translations:

• A translation left by 1 unit modifies the function inside the absolute value by adding 1: $f(x + 1)$.
• A translation up by 2 units adds 2 to the entire function: $f(x + 1) + 2$.

Therefore, the new function $g(x)$ becomes: $g(x) = |x + 1| + 2$

The correct answer is: $\boxed{g(x) = |x + 1| + 2}$

Would you like more details on this? Here are five related questions to expand on this topic:

1. What happens to the graph of $f(x) = |x|$ when translated down 3 units?
2. How does translating right by 2 units affect $f(x) = |x|$?
3. What is the general form of a function translated left by $h$ units and up by $k$ units?
4. How do reflections affect the absolute value function $f(x) = |x|$?
5. Can horizontal and vertical stretches or compressions be combined with translations?

Tip: Translations inside the absolute value modify the $x$-axis movements, while changes outside affect vertical movements!