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$\renewcommand{\d}{\displaystyle}\newcommand{\N}{\mathbb N}$

Suppose $f:\N \to \N$ satisfies the recurrence $f(n+1) = f(n) + 3\text{.}$ Note that this is not enough information to define the function, since we don’t have an initial condition. For each of the initial conditions below, find the value of $f(5)\text{.}$

$f(0) = 0\text{.}$
$f(5) =$

$f(0) = 1\text{.}$
$f(5) =$

$f(0) = 2\text{.}$
$f(5) =$

$f(0) = 100\text{.}$
$f(5) =$