Answer
$f(x)$ is linear, $g(x)$ is not
$f(x)=4x+6$
Work Step by Step
For linear functions,
a change of $\Delta x$ units in results in a change of $\Delta y=m\Delta x$ units in $y$.
The table shows changes in x of $\Delta x=+1$, (constant throughout the row)
so
the linear function will have constant changes, $\Delta y$.
f(x) has constant changes , $\Delta y$=4 so it is linear.
g(x) has consecutive $\Delta y$ of 2,2,4,6 ... not constant, so it is not linear
The equation of f is of the form $f(x)=mx+c$,
(m=slope, b=y-intercept)
From this table, for every change in x of $\Delta x=+1$,
the change in y=f(x), $\Delta y=+4$, so
$m=\displaystyle \frac{4}{1}=4. $
The table also gives $b=f(0)=6$ (the y-intercept)
So, $f(x)=mx+c$,
$f(x)=4x+6$
