Final answer:
Without specific information about the function g(x), it is impossible to provide a direct answer regarding its continuity. Continuity involves the function being defined and its limit matching the function's value, which requires analytical or graphical data for determination.
Step-by-step explanation:
The direct answer to the question concerning the continuity of the function g(x) is not possible to determine from the given information. There is insufficient data to unequivocally state whether g(x) is continuous everywhere, has a jump or removable discontinuity, or is undefined. To assess the continuity of g(x), specific details about the function's behavior or its graph would be required.
To explain continuity, let's consider a function f(x). If f(x) is defined at a point x, and the limit of f(x) as x approaches that point is equal to the function's value at that point, then f(x) is said to be continuous at that point. This indicates that the graph of f(x) has no breaks, jumps, or holes at that point. A function with a jump discontinuity will have a sudden change in value, often visible as a 'jump' in the graph. A function with a removable discontinuity has a hole in the graph that can be 'removed' by redefining the function's value at that point. Lastly, if a function is not defined for at least one value in its domain, we can say it is undefined at those points, and it may not be continuous.
A displacement versus time plot that is linear indicates that the function describing displacement doesn't change direction or curvature, implying that the acceleration is zero, as acceleration would be the second derivative of such a function with respect to time.