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We are asked to find a function \( g(x) \) that represents two transformations applied to the graph of \( f(x) = x + 1 \):

1. A reflection in the **x-axis**.
2. A translation **3 units up**.

### Step-by-step solution:
1. **Reflection in the x-axis**:
   - Reflecting a graph in the x-axis means multiplying the output (or \( y \)-values) of the function by \(-1\). 
   - Applying this to \( f(x) = x + 1 \), we get:
     \[
     g(x) = -(x + 1) = -x - 1
     \]

2. **Translation 3 units up**:
   - To translate the graph 3 units upward, we add 3 to the function:
     \[
     g(x) = (-x - 1) + 3
     \]
   - Simplifying this:
     \[
     g(x) = -x + 2
     \]

Thus, the function after both transformations is \( g(x) = -x + 2 \).

### Now, looking at the answer choices:
The correct option is **g(x) = -x + 1 + 3**, which simplifies to **g(x) = -x + 2**.

This corresponds to the third option in the list.

### Do you have any questions or want further details?

### Related Questions:
1. What would happen if the graph was translated down instead of up?
2. How would the function change if the reflection was in the y-axis instead of the x-axis?
3. What is the general form of a function reflection across the x-axis?
4. Can you describe how translations work with parabolas?
5. How do vertical stretches or compressions affect the graph of a function?

**Tip:** When performing reflections and translations, apply reflections first, then translations, as translations modify the position after the reflection transformation.

Write a function g whose graph represents a reflection in the x-axis followed by a translation 3 units up of the graph of f(x) = |x + 1|.

Learn how to reflect and translate the graph of an absolute value function. This question guides you through reflecting f(x) = |x + 1| across the x-axis and then translating it 3 units up to find the new function g(x). Suitable for students in Grades 9-12.

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