One of the two sets of functions, $f_1$, $f_2$, $f_3$, or $g_1$, $g_2$, $g_3$, is graphed in the figure to the left below; the other set is graphed in the right figure. Points $A$ and $B$ each have $x=0$. Taylor polynomials of degree 2 approximating these functions near $x=0$ are as follows: $$f_1(x) \approx 2+x-x^{2} \qquad\qquad g_1(x) \approx 2+x+2x^{2}$$ $$f_2(x) \approx 2+x+2x^{2} \qquad\qquad g_2(x) \approx 2-x+x^{2}$$ $$f_3(x) \approx 2+x+x^{2} \qquad\qquad g_3(x) \approx 2+x+x^{2}.$$

(a) Match the functions to the appropriate figure:
$f$ matches ? I II
$g$ matches ? I II

(b) What are the coordinates of the points $A$ and $B$?
$A =$
$B =$

(c) Match each function with the graphs (a)--(c) in the appropriate figure.
$f_1 =$ ? I.a I.b I.c II.a II.b II.c
$f_2 =$ ? I.a I.b I.c II.a II.b II.c
$f_3 =$ ? I.a I.b I.c II.a II.b II.c
$g_1 =$ ? I.a I.b I.c II.a II.b II.c
$g_2 =$ ? I.a I.b I.c II.a II.b II.c
$g_3 =$ ? I.a I.b I.c II.a II.b II.c