To determine the value of \( k \) that would characterize the horizontal shift in the demand curve from \( y = f(x) \) to \( y = f(x - k) \), we need to look at the horizontal distance between the two lines plotted on the coordinate plane.
The left line, representing \( y = f(x) \), will be the original demand curve, and the right line, representing \( y = f(x - k) \), will be the shifted curve. The parameter \( k \) indicates how far the curve has shifted to the right or left.
If the curve shifts to the right, it means that for a given price level, more units are now being demanded. The distance between the two curves along the x-axis will help us determine \( k \).
You would look for the specific x-value on the original curve and see where the new curve intersects vertically with the y-axis at the same price point. This distance will represent the value of \( k \).
Since I can't see the image, I can't determine the exact value. However, if you can identify from the graph how far the left curve is to the right on the x-axis to hit the same price level as in the left curve, that would give you the value of \( k \).
For example, if the line to the right intersects at an x-value of 10 where the left line intersects at an x-value of 0, then \( k = 10 \).
So if it was shown that the left line intersects at, say, 20 and the right line intersects at 10, then the shift would be \( 20 - 10 = 10 \), thus \( k = 10 \).
Similarly, you would apply the same reasoning to find the correct value of \( k \) based on the data represented in the image.
Based on typical horizontal shifts from such scenarios, it may be approximately one of the given options: \( 10, 5, 2, \text{or } 8. \)
Please check the graph for the x-values of the intersecting points to determine which value represents \( k \) correctly.
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