Understanding left-hand and right-hand limits helps us see how functions act near certain points.

1. Left-Hand Limit ($\lim_{x \to a^-} f(x)$): This tells us what value the function gets close to when we approach $a$ from the left side.

2. Right-Hand Limit ($\lim_{x \to a^+} f(x)$): This shows us what the function gets close to when we approach $a$ from the right side.

By looking at both limits, we can find out if a function has a jump or if it is smooth and continuous at that spot.

Think of it like checking both sides of a door before opening it!