$A$ function $f$ is defined by $f(x) = 2x - 5$. Find the values of $f(0)$,$f(7)$,and $f(-3)$.

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?

The relation $f$ is defined by $f(x) = \begin{cases} x^2, & 0 \le x \le 3 \\ 3x, & 3 \le x \le 10 \end{cases}$. The relation $g$ is defined by $g(x) = \begin{cases} x^2, & 0 \le x \le 2 \\ 3x, & 2 \le x \le 10 \end{cases}$. Show that $f$ is a function and $g$ is not a function.

Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)\}$

Examine the following relation and state whether it is a function or not,giving reasons:
$R = \{(2, 1), (3, 1), (4, 2)\}$

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.