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Is it true that If an odd function has zero in its domain, then it must pass through the origin. (Hint: $0$ is in the domain, we can apply $f(-x) = -f(x)$ at $x=0$) 
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By definition of an odd function, $f(-x) = -f(x)$ for all $x$ in the domain. Since $x = 0$ is in the domain, we have $f(-0) = -f(0)$, which means $f(0) = -f(0)$, or $2f(0) = 0$, and thus $f(0) = 0$ (this represents the origin). 