To determine the value of \( k \) that represents the horizontal shift from the graph of \( y = f(x) \) to \( y = f(x - k) \), we need to consider how the function is transformed.
For the function \( y = f(x - k) \):
- If \( k > 0 \), the graph shifts to the right by \( k \) units.
- If \( k < 0 \), the graph shifts to the left by \( |k| \) units.
From the problem, we need to identify the correct value of \( k \) based on the horizontal shift observed in the graph.
Without the visual of the graph, let’s analyze the options provided:
- If the line to the right of \( y = f(x) \) indicates a shift to the right, we would choose a positive \( k \) (5, 10, 8, or 2).
- If the line indicates a shift left, we would choose a negative \( k \).
Typically, if you have specific numerical shifts indicated, you would select the value that corresponds to the observed shift.
Final Answer:
Assuming the shift is to the right (since no direction of the shift is given in the problem), the possible values can be concluded as:
- 5
- 10
- 8
- 2
Without knowing the exact shift from the graph, it is impossible to provide the exact answer. However, analyze the graph and choose the option corresponding to the observed horizontal movement.
If the graph has a rightward shift of 10 units, then the answer is \( k = 10 \).
If you provide the direction or distance of the shift from the graph, I could confirm the value of \( k \).