Answer
$f(x)=3x+3$
Work Step by Step
The function is linear, we are told, so
$y=f(x)=mx+b$
(m=slope, b=y-intercept)
For linear functions,
a change of $\Delta x$ units in results in a change of $\Delta y=m\Delta x$ units in $y$
From this table,
For every change in x of $\Delta x=1$,
the change in y=f(x), $\Delta y=+3$, so
$m=\displaystyle \frac{3}{1}=3. $
The table gives us: $f(0)=3 ,$ which gives us $b=3$
Therefore,
$f(x)=3x+3$
