To determine the value of \( k \) for the horizontal shift in the function, we need to identify the nature of the shift between the original function and the translated (shifted) function.
In the case of the transformation \( y = f(x - k) \), a positive \( k \) indicates a shift to the right, while a negative \( k \) indicates a shift to the left.
If you can observe the change in the graph, such as the leftmost point or vertex of each parabola, you can calculate \( k \) by comparing the x-coordinates before and after the shift. If, for example, the vertex of the original \( y = f(x) \) was at \( x = 0 \) and in the translated function it is now at \( x = 3 \), then \( k \) would be calculated as follows:
\[ k = x_{\text{original}} - x_{\text{translated}} = 0 - 3 = -3 \]
Conversely, if the original vertex were at \( x = -3 \) and shifted to \( x = 0 \), then:
\[ k = -3 - 0 = -3 \]
Without the actual images, it's not possible to definitively state the value of \( k \), but you can conclude that the value of \( k \) is equal to the difference in the x-coordinate of the vertex or any distinguished point on the parabolas before and after the shift.
Please determine the details from the images to find the exact \( k \) based on the shift direction and magnitude noted.
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