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To solve this problem, we need to determine the value of \( k \) that transforms the graph of \( f(x) = 0.5x - 4 \) into the graph of \( g(x) \). The transformation is given by \( g(x) = f(x - k) \), which represents a horizontal shift of \( k \) units. 

### Steps to Solve
1. **Identify the Shift from the Graphs:**
   - The graph of \( f(x) = 0.5x - 4 \) is shown as the blue line.
   - The graph of \( g(x) \) (the transformed function) is the red line.
   
2. **Determine Key Points:**
   - Observe any two specific points on \( f(x) \) and \( g(x) \) to see how far they are horizontally shifted.
   - For example, you could compare the x-intercepts or y-intercepts of the two lines.

3. **Calculate the Horizontal Shift \( k \):**
   - The function \( g(x) = f(x - k) \) implies that every point on \( f(x) \) is shifted \( k \) units to the right to match \( g(x) \).
   - Based on the graph, observe the distance along the x-axis between corresponding points of \( f(x) \) and \( g(x) \).

From a visual check, it appears that the blue line (graph of \( f(x) \)) is shifted **4 units to the right** to match the red line (graph of \( g(x) \)). Thus, \( k = 4 \).

### Answer
The value of \( k \) that transforms the graph of \( f(x) \) into \( g(x) \) is:
\[
k = 4
\]

Would you like a detailed explanation of transformations or have any questions?

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Here are some related questions for further exploration:

1. How does a horizontal shift affect the x-coordinates of a function's points?
2. What would happen to the graph if we used \( g(x) = f(x + k) \) instead?
3. How does changing the slope in \( f(x) = 0.5x - 4 \) affect the transformation?
4. What other types of transformations can be applied to functions, besides horizontal shifts?
5. How would we calculate \( k \) if the transformation involved both a horizontal and a vertical shift?

**Tip:** When identifying transformations, focus on how points like intercepts or key points shift to determine the values for transformations like \( k \) in horizontal shifts.

What value of k transforms the graph of f(x) = 0.5x - 4 into the graph g? Use the graph and the given equation to describe the transformation.

Learn how to find the horizontal shift value k that transforms the graph of f(x) = 0.5x - 4 into another graph using a horizontal transformation equation. This problem explores function transformations, focusing on linear functions and shifts.

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