4. As shown in Figure $1, f(x)$ is a function defined on the interval $[-4$, 4] and is an odd function. Let $g(x)=a f(x)+b$. Then, among the following statements about $g(x)$, the correct one is ( ).
(A) If $a<0$, then the graph of the function $g(x)$ is symmetric with respect to the origin
(B) If $a=-1,-2<b<0$, then the equation $g(x)$ $=0$ has a real root less than 2
(C) If $a \neq 0, b=2$, then the equation $g(x)=0$ has two real roots
(D) If $a \geqslant 1, b<0$, then the equation $g(x)=0$ has three real roots
4.B.

If $a=-1$, the graph of $f(x)$ is reflected over the $x$-axis to get $-f(x)$; if $-2<b<0$, the graph of $-f(x)$ is translated downward along the $y$-axis by $|b|$ units, then there are real roots less than 2.