Answer
$g(x)$ is linear, $f(x)$ is not
$g(x)=\displaystyle \frac{1}{2}x-4$
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$0,
(constant throughout the row)
so
the linear function will have constant changes of y, $\Delta y$.
f(x) has consecutive $\Delta y$ of $\ \ 1.5, 1.5, 1.0, 1.0$ ... not constant, so it is not linear
g(x) has consecutive $\Delta y$ of 5,5,5,5 ... constant, therefore g is linear
The equation of g is of the form $f(x)=mx+c$,
(m=slope, b=y-intercept)
From this table, for every change in x of $\Delta x=+10$,
the change in y=f(x), $\Delta y=+5$, so
$m=\displaystyle \frac{5}{10}=\frac{1}{2}. $
The table also gives $b=g(0)=-4$ (the y-intercept)
So, $g(x)=mx+c$,
$g(x)=\displaystyle \frac{1}{2}x-4$
