Finding limits from graphs

DEFINITION:
left-hand limit: $\lim_{x \to a^-} f(x) = L$
We say "the limit of f(x), as x approaches a from the negative direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the left, but x is not equal to a.

DEFINITION:
right-hand limit: $\lim_{x \to a^+} f(x) = L$
We say "the limit of f(x), as x approaches a from the positive direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the right, but x is not equal to a.

DEFINITION:
$\lim_{x \to a} f(x) = L$ if and only if $\lim_{x \to a^+} f(x) = L$ and $\lim_{x \to a^-} f(x) = L$