Does an odd function always pass through the origin?

Answer 1

an odd function is symmetric about the origin,

f(-x) = -f(x)

if (1,2) is in f(x) then (-1,-2) is also in f(x)

but the origin doesn't have to be in the function.

y=1/x is symmetric about the origin, and is an odd function, but (0,0) is not in the function