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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!

Given the function f(x) = |x|, write the function if f(x) was translated left 1 unit and up 2 units.

Learn how to translate the absolute value function f(x) = |x| left 1 unit and up 2 units. This problem covers key concepts such as function translation formulas and the effects on the graph of an absolute value function. Suitable for students in Grades 9-11.

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