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.