Explanation:
To determine the value of k based on the graph of f(x) and the table for g(x) = f(kx), you need to look at how the graph of g(x) is related to the graph of f(x). Specifically, you want to find the value of k that scales or stretches the graph of f(x) to match the graph of g(x).
If k = 1/4, it means g(x) = f(1/4 * x), which would compress or shrink the graph horizontally by a factor of 4. This would make the graph of g(x) narrower than f(x).
If k = 4, it means g(x) = f(4 * x), which would stretch the graph horizontally by a factor of 1/4. This would make the graph of g(x) wider than f(x).
If k = 1/8, it means g(x) = f(1/8 * x), which would compress or shrink the graph horizontally by a factor of 8. This would make the graph of g(x) much narrower than f(x).
If k = -8, it means g(x) = f(-8 * x), which would also stretch the graph horizontally by a factor of 1/8. This would make the graph of g(x) wider than f(x), but in the opposite direction compared to k = 4.
So, the correct value of k depends on how the graph of g(x) compares to the graph of f(x), and it could be either k = 4 or k = -8, depending on the specific details of the graph and table provided.