Final answer:
To determine if f(x) or g(x) increases faster without equations, we need to compare their rates of increase using a graph. The investment that has a graph with a steeper slope is increasing faster. Without the graphs, we need more information to answer the question correctly.
Step-by-step explanation:
To determine which investment option, f(x) or g(x), increases faster, we would typically look at the derivatives of these functions if we have their equations, but here we are asked to use a graph for the explanation. In the context of investments, an increase in value is shown by the slope of the line or the curve on the graph. A steeper slope indicates a faster increase.
When constructing a double time series graph with a common x-axis, we are effectively comparing the rate at which both f(x) and g(x) change over time. The rate at which they increase can then be visualized by seeing which graph rises more steeply as time progresses. If one graph consistently rises faster than the other, we can say that investment option has a higher growth rate.
Without the actual graphs or more information, we cannot conclusively say which investment option increases faster. Therefore, the correct answer to the question is D) I need more information.