Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)\}$

Let $N$ be the set of natural numbers and the relation $R$ be defined on $N$ such that $R = \{(x, y) : y = 2x, x, y \in N \}$. What is the domain,codomain,and range of $R$? Is this relation a function?

Let $f$ be the subset of $Z \times Z$ defined by $f = \{(ab, a+b) : a, b \in Z\}$. Is $f$ a function from $Z$ to $Z$? Justify your answer.

Let $A = \{a, b, c, d\}$ and $B = \{1, 2, 3\}$. The relations $R_1, R_2, R_3, R_4$ are defined as follows:
$R_1 = \{(a, 1), (b, 2), (c, 1), (d, 2)\}$
$R_2 = \{(a, 1), (b, 1), (c, 1), (d, 1)\}$
$R_3 = \{(a, 2), (b, 3), (c, 2), (d, 2)\}$
$R_4 = \{(a, 1), (b, 2), (a, 2), (d, 3)\}$
Which of the following is true?

If $Q$ denotes the set of all rational numbers and $f\left(\frac{p}{q}\right)=\sqrt{p^2-q^2}$ for any $\frac{p}{q} \in Q$, then observe the following statements.
$I$. $f\left(\frac{p}{q}\right)$ is real for each $\frac{p}{q} \in Q$.
$II$. $f\left(\frac{p}{q}\right)$ is a complex number for each $\frac{p}{q} \in Q$.
Which of the following is correct?

Let $N$ be the set of natural numbers. Define a function $f: N \rightarrow N$ by $f(x) = 2x + 1$. Using this definition,complete the table given below.

$x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$y$	$f(1) = \dots$	$f(2) = \dots$	$f(3) = \dots$	$f(4) = \dots$	$f(5) = \dots$	$f(6) = \dots$	$f(7) = \dots$