Mathematics

This problem is about understanding one-sided limits and how absolute value behaves differently on each side of zero. When $x$ approaches 0 from the left, $x$ is negative, so $|x| = -x$—this flips the sign. The key insight is to simplify $f(x)$ using this fact for negative values, then see what constant value the function actually equals as you get arbitrarily close to zero from that side.

This problem is about understanding one-sided limits and how absolute value behaves differently on each side of zero. When $x$ approaches 0 from the left, $x$ is negative, so $|x| = -x$—this flips the sign. The key insight is to simplify $f(x)$ using this fact for negative values, then see what constant value the function actually equals as you get arbitrarily close to zero from that side.