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Describe the transformation in g(x)=x+4g(x)=x+4 as it relates to the graph of the parent function.
 
vertical translation: 1 of 4.Select Choice4 units up4 units downnone

horizontal translation: 2 of 4.Select Choice4 units left4 units rightnone

dilation: 3 of 4.Select Choicevertical stretch by a factor of 4vertical stretch by a factor of 0.25vertical compression by a factor of 4none

reflection: 4 of 4.Select Choiceacross the x-axisacross the y-axisnone  solve

Let's analyze the transformation in the function \( g(x) = x + 4 \) based on the parent function \( f(x) = x \), which is a simple linear function with a slope of 1.

### Breakdown of the Transformations
1. **Vertical Translation**: 
   The function \( g(x) = x + 4 \) includes an addition of 4 outside the \( x \)-variable. This indicates a **vertical translation of 4 units up**.

2. **Horizontal Translation**: 
   There is no change to the \( x \)-variable itself (i.e., there's no addition or subtraction within \( x \)), so there is **no horizontal translation**.

3. **Dilation**:
   There is no coefficient change to \( x \), so the slope remains 1. Thus, there is **no dilation**.

4. **Reflection**: 
   The function has no negative sign in front of \( x \) or outside the entire expression, so there is **no reflection**.

### Answer Choices:
- **Vertical Translation**: 4 units up
- **Horizontal Translation**: none
- **Dilation**: none
- **Reflection**: none

Would you like further explanation on this transformation? 

Here are some related questions to expand your understanding:
1. What transformation occurs if the function is \( g(x) = x - 3 \)?
2. How does a negative sign in front of \( x \) in \( g(x) = -x \) affect the graph?
3. What happens to the graph if a coefficient is added, as in \( g(x) = 2x + 4 \)?
4. How would a horizontal shift of 5 units right affect the function \( g(x) = x \)?
5. Can a function have both a vertical and horizontal transformation at the same time?

**Tip:** When analyzing transformations, start by identifying if constants are added/subtracted to \( x \) for horizontal shifts and to \( g(x) \) for vertical shifts.

Describe the transformation in g(x) = x + 4 as it relates to the graph of the parent function.

Explore how the function g(x) = x + 4 is transformed from its parent function f(x) = x. This problem involves analyzing vertical translations, horizontal translations, dilation, and reflection for linear functions, suitable for Grades 8-10.

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