Select all the correct answers.
Compare the functions below.

f(x) + 3^x + 2
g(x) = 20x + 4
h(x) = 2x^2 + 5x +2

Select the true statements.

A. Over the interval [2, 3], the average rate of change of g is lower than that of both f and h.
B. When x > 4, the value of f(x) exceeds the values of both g(x) and h(x).
C. As x increases on the interval [0, ∞), the rate of change of g eventually exceeds the rate of change of both f and h.
D. A quantity increasing exponentially eventually exceeds a quantity growing quadratically or linearly.
E. When x ≈ 8, the value of h(x) exceeds the values of both f(x) and g(x).
F. As x increases on the interval [0, ∞), the rate of change of f eventually exceeds the rate of change of both g and h.