Since f(x) is a polynomial function and g(x) is an exponential function, we know that both the value and the rate of change of g(x) will exceed those of f(x) when x gets large.
The rate of change of g(x) is less than that of f(x) for x < 3.4. The value of g(x) is less than that of f(x) for x < 4.39. Of the statements offered, the only one that is true is ...
... As x increases, the rate of change of g exceeds the rate of change of f.
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In the attached graph, the functions are graphed as solid lines; their rates of change are graphed as dashed lines of the same color.
