Which of the following is definitely false?

The graph of the $f(x)$ function is given above.

According to this graph, which of the following is definitely false?

A) $\lim_{x\to -2}f(x)=1$

B) $\lim_{x\to 2^+}f(x)+\lim_{x\to 0}f(x)=4$

C) $f(x)$ is defined at $x=2$

D) $\lim_{x\to 2^-}f(x)+\lim_{x\to 0^-}f(x)=7$

E) $\lim_{x\to -2}f(x)+f(2)=-1$

My attempts:

At first, I couldn't understand the difference between false and definitely false.

A) is correct. Because, $\lim_{x\to -2^+}f(x)=\lim_{x\to -2^-}f(x)=1$.

B) I get, $\lim_{x\to 2^+}f(x)+\lim_{x\to 0}f(x)=1+2=3$

C) is correct. Because, it is black for the circle.

D) I get

$\lim_{x\to 2^-}f(x)+\lim_{x\to 0^-}f(x)=5+2=7$

E) I get

$\lim_{x\to -2}f(x)+f(2)=1+1=2$.

Thus, several options are definitely false. ( B and E). Where am I doing wrong?

Checking your answers:

A) Correct, it looks true.
B) Correct, it is definitely false.
C) Correct, it looks true.
D) Correct, it looks true.
E) Correct, it is definitely false.

Looks good.