In the context of motion on a graph, "no movement" typically refers to a range of x-values where the object does not change its position. This would correspond to a horizontal line segment or a flat section on the graph indicating that the y-value (position) remains constant over that range of x-values.
Let's analyze the provided options:
- −2 ≤ x ≤ 1: This could potentially indicate movement if the y-values change during this interval.
- −5 ≤ x ≤ 5: This range encompasses all x-values on the graph, suggesting there could be movement throughout this entire span.
- 1 ≤ x ≤ 4: Similar to option 1, this might indicate movement depending on the y-values.
- −5 ≤ x ≤ −2: This is a restricted interval where the object may be stationary depending on the y-value for the corresponding x-values.
From the options, if we are looking for a range where the object shows no movement, it is most likely that none of these options explicitly indicate a situation of no movement without additional context regarding the corresponding y-values.
However, typically, if we analyze them based on general understanding, option 3 (1 ≤ x ≤ 4) might often be associated with motion, and option 2 encompasses all possible movement. Therefore, if any flat section exists, it might be narrow.
Given the lack of specific y-value descriptions, the best answer among the options would be:
−5 ≤ x ≤ −2
This range implies a more restricted area, which might be the one where movement is potentially indicated less unless there's more context about where the y-values lie.