For each of the following functions \(f\), say whether \(f\) is 1-1 and whether \(f\) is onto:

(i) \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined by \(f(x)=x^{2}+2 x\) for all \(x \in \mathbb{R}\).

(ii) \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined by

\[ f(x)=\left\{\begin{array}{l} x-2, \text { if } x>1 \\ -x, \text { if }-1 \leq x \leq 1 \\ x+2, \text { if } x<-1 \end{array}\right. \]

(iii) \(f: \mathbb{Q} \rightarrow \mathbb{R}\) defined by \(f(x)=(x+\sqrt{2})^{2}\).

(iv) \(f: \mathbb{N} \times \mathbb{N} \times \mathbb{N} \rightarrow \mathbb{N}\) defined by \(f(m, n, r)=2^{m} 3^{n} 5^{r}\) for all \(m, n, r \in \mathbb{N}\).

(v) \(f: \mathbb{N} \times \mathbb{N} \times \mathbb{N} \rightarrow \mathbb{N}\) defined by \(f(m, n, r)=2^{m} 3^{n} 6^{r}\) for all \(m, n, r \in \mathbb{N}\).

(vi) Let \(\sim\) be the equivalence relation on \(\mathbb{Z}\) defined by \(a \sim b \Leftrightarrow\) \(a \equiv b \bmod 7\), and let \(S\) be the set of equivalence classes of \(\sim\). Define \(f: S \rightarrow S\) by \(f(\operatorname{cl}(s))=\operatorname{cl}(s+1)\) for all \(s \in \mathbb{Z}\).