Answer
$f(x)=-x-5$
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), $\Delta y=+1$, so
$m=\displaystyle \frac{1}{-1}=-1. $
From "Computing the y-Intercept of a Line":
the y-intercept of the line passing through $(x_{1},y_{1})$ with slope $m$ is
$b=y_{1}-mx_{1}$
which gives us, inserting $(x_{1},y_{1})=(-4,-1)$
$b=-1-(-1)(-4)=-5$
Therefore,
$f(x)=mx+b$
$f(x)=-x-5$
