Answer
See the graph
Work Step by Step
We are given: $f(x)=0.5x-4$
Domain: $\{-4,-2,0,2,4\}$
Let's make a list of values:
$x=-4 \rightarrow y=-6$
$x=-2 \rightarrow y=-5$
$x=0 \rightarrow y=-4$
$x=2 \rightarrow y=-3$
$x=4 \rightarrow y=-2$
The graph consists of separate points, so the function is discrete.
The range is $\{-6,-5,-4,-3,-2\}$.