Suppose $f$ is a continuous function on $-2,2$ such that

$f(-2)=1,f(2)=-1$

Which of the properties below follow without further restriction on $f$ by applying the $-$

A$.$ the graph of $f(x)+x$ crosses the $x-$axis

B$.f^2(c)=\frac{1}{4}$ for some $c$ in $(-2,2)$;

C$.f(c)=0$ for some $c$ in $(-1,1).$

X$1.$ all of them

$2.$ A and B only

$3.$ A only

$4.$ B only

$5.$ B and C only

$6.$ C only

$7.$ none of them

$8.$ A and C only