Answer
See the graph
Work Step by Step
We are given: $y=2x+3$
Domain: $\{-2,-1,0,1,2\}$
Let's make a list of values:
$x=-2 \rightarrow y=-1$
$x=-1 \rightarrow y=1$
$x=0 \rightarrow y=3$
$x=1 \rightarrow y=5$
$x=2 \rightarrow y=7$
The graph consists of separate points, so the function is discrete.
The range is $\{-1,1,3,5,7\}$.