To determine the value of \( k \) that represents the horizontal shift between the two lines \( y = f(x) \) and \( y = f(x - k) \), we need to look at the graph for the x-intercepts of both curves.
The line representing \( y = f(x) \) is the original demand curve, and the line representing \( y = f(x - k) \) is the curve shifted to the right by \( k \) units.
By examining the x-axis values of where the two lines intercept the x-axis (where \( y = 0 \)), we can calculate the value of \( k \):
- If the left curve (where \( y = f(x) \)) intercepts the x-axis at a particular point, and the right curve (where \( y = f(x - k) \)) intercepts at a value that is \( k \) units to the right of that point.
For example:
- If the left curve intercepts at \( 10 \) and the right curve intercepts at \( 20 \), then the value of \( k \) would be \( 20 - 10 = 10 \).
Based on the given options, you will need to determine the specific intercepts from the graph. If you find the intercept values on the graph, simply subtract the left point from the right point to find \( k \).
Considering possible intercepts, the value of \( k \) could be among the listed options: 2, 10, 8, 5.
Please closely analyze the graph's intercepts to identify the correct value for \( k \), and select that option.