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The problem asks you to find the new function \( g(x) \) when the function \( f(x) = |x| \) is translated 1 unit to the left and 2 units up.

### Translation steps:
1. **Left 1 unit**: When you translate a function to the left, you add to the \( x \)-value inside the absolute value. This means the transformation for shifting left 1 unit is \( |x + 1| \).
2. **Up 2 units**: When you translate a function up, you add to the entire function. So, adding 2 to the function results in \( |x + 1| + 2 \).

Thus, the translated function \( g(x) = |x + 1| + 2 \).

### The correct answer is:
- \( g(x) = |x + 1| + 2 \) (Option B)

Would you like further details on transformations? 

Here are some follow-up questions:
1. What is the effect of shifting the function to the right instead of the left?
2. How do you translate a function down instead of up?
3. How do reflections affect the graph of an absolute value function?
4. What happens when you multiply the absolute value function by a negative number?
5. How does scaling the function vertically affect its shape?

**Tip:** Always remember, horizontal translations affect the \( x \)-values, while vertical translations affect the entire function.

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

Learn how to transform the function f(x) = |x| by translating it 1 unit to the left and 2 units up. This problem introduces the concept of horizontal and vertical translations of absolute value functions, suitable for students in Grades 9-12.

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