To determine the value of k that characterizes the horizontal shift in the demand curve, we can analyze the graphs of \( y = f(x) \) and \( y = f(x-k) \).
In a horizontal shift of the demand curve, if \( y = f(x-k) \) is to the right of \( y = f(x) \), then k represents the amount of the shift to the right.
Based on the description, if the line to the left represents \( y = f(x) \) and the line to the right represents \( y = f(x-k) \), we need to find out how far the right line has moved compared to the left line.
Assuming you are looking for the amount of units that the demand curve shifted to the right, you will look along the x-axis values.
Here are the options given:
- 2
- 10
- 5
- 8
To find the exact value of k, we would typically inspect the graph directly to see how many units the line shifted to the right. Since I cannot see the graph, I cannot provide a definitive answer. However, if you have the specific x-axis values for both lines in front of you, the correct value of k would be the difference between the x-coordinate of the right line (i.e., \( f(x-k) \)) and the x-coordinate of the left line (i.e., \( f(x) \)).
If you can identify that difference, you would select that value from the options provided. Without the graph, you would choose the corresponding answer based on your observation.