  We give a unateness tester for functions of the form $f:[n]^d\rightarrow R$,
where $n,d\in \mathbb{N}$ and $R\subseteq \mathbb{R}$ with query complexity
$O(\frac{d\log (\max(d,n))}{\epsilon})$. Previously known unateness testers
work only for Boolean functions over the domain $\{0,1\}^d$. We show that every
unateness tester for real-valued functions over hypergrid has query complexity
$\Omega(\min\{d, |R|^2\})$. Consequently, our tester is nearly optimal for
real-valued functions over $\{0,1\}^d$. We also prove that every nonadaptive,
1-sided error unateness tester for Boolean functions needs
$\Omega(\sqrt{d}/\epsilon)$ queries. Previously, no lower bounds for testing
unateness were known.
