To determine the value of \( k \) that represents the horizontal shift in the demand curve, we need to understand how the function \( y = f(x) \) shifts to the right to become \( y = f(x - k) \).
In general, a function \( f(x - k) \) represents a shift to the right by \( k \) units on the x-axis. This means if you observe the two line segments plotted on the graph, the distance between the two horizontal demands (from the point of intersection) on the x-axis will be equal to \( k \).
Based on the description of your coordinate plane not being directly visible here, if you have marked points or segments, simply look at how far apart the two lines are horizontally.
If the left demand curve intersects the x-axis at a certain point and the right demand curve intersects at that point plus or minus a certain value, that value is the correct \( k \).
From the options provided—2, 5, 8, or 10—the value of \( k \) can be inferred from the graph itself based on the distance between the endpoints of the segments.
However, since I can't see the graph, I would suggest you measure the horizontal distance between the two vertical intercepts of the lines directly on the graph. The response corresponding to that distance will give you the correct \( k \).
If you'd like, you can describe the graph, and I can assist you in narrowing down which option best fits the observed horizontal shift.
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