Domain Matters For Continuity

The mathematical horror story no one asked for! Left side shows sine function, smooth and well-behaved like that student who always turns in homework early. Right side? That's tangent with its vertical asymptotes—basically math having an existential crisis every π radians.

Both functions are technically "continuous" where they're defined, but tangent has these dramatic infinity vacations where it simply refuses to exist. It's the function equivalent of saying "Sorry, can't come to work today, busy approaching infinity."

The faces perfectly capture the vibe—sine is living its best life with complete domain, while tangent is having war flashbacks from all those calculus problems where students forgot about its domain restrictions. Trust me, I've seen grown mathematicians cry when someone casually asks about the continuity of tan(π/2).