Answer
$f(x)=2x-2$
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), $\displaystyle \Delta y=2,$ so $m=\frac{2}{1}=2. $
The table gives us: $f(0)=-2 ,$ which gives us $b=-2$
Therefore,
$f(x)=2x-2$
