The line tangent to the graph of $g(x) = x^{3}-4x+1$ at the point $(2, 1)$ is given by the formula $$L(x) = 8(x - 2) + 1.$$ These functions are graphed below.

Which of the following statements are true? Select all that apply.

A. The functions are approximately equal on the interval $0.5 \leq x \leq 1.0$.

B. The slope of the line equals $g'(0)$.

C. The slope of the line equals $g'(2)$.

D. The functions are approximately equal on the interval $1.9 \leq x \leq 2.1$.

E. The graphs intersect at the point $(2,1)$.

F. The functions have the same $y$-intercept.

G. None of the above are true.