Final answer:
To determine which function is the derivative of the other, we need to analyze the characteristics of their graphs. Based on the given graph, it is more likely that h(x) is the derivative of g(x). However, without further information, we cannot conclusively determine the relationship between the functions.
Step-by-step explanation:
In order to determine which of the two functions, g(x) or h(x), is the derivative of the other, we need to analyze the features of their graphs. If g(x) is the derivative of h(x), then the graph of g(x) will represent the slope of the graph of h(x). This means that the slopes of h(x) will correspond to the y-values of g(x) for each x-value. On the other hand, if h(x) is the derivative of g(x), then the graph of h(x) will represent the slope of the graph of g(x), meaning that the slopes of g(x) will correspond to the y-values of h(x) for each x-value.
By closely examining the given graph of the two functions, we can see that the dashed curve represents a smooth, continuously increasing or decreasing function. This implies that it is more likely to be the derivative function since it reflects the changing slopes of the solid curve. The solid curve, on the other hand, may represent a more complex function that is derived from the derivative function.
In conclusion, based on the characteristics of the graphs, it is likely that h(x) is the derivative of g(x), meaning that h(x) = g'(x). However, without additional information about the specific equations of the functions or their behaviors, we cannot definitively determine the relationship between the two functions.