it is easier to see this in the graph
So we can give values to X and look the graph
[tex]\begin{gathered} x=-2\longrightarrow\text{ y=7} \\ x=-1\longrightarrow y=6 \\ x=0\longrightarrow y=5 \\ x=1\longrightarrow y=4 \\ x=2\longrightarrow y=3 \\ x=3\longrightarrow y=4 \end{gathered}[/tex]the graph is something like this
and the range is all the values it can take in Y
From the graph we observe that values less than 3 will not be taken because the function is a absolute value
And it will only take values greater than 3
So the range is:
[tex]\lbrack3,\infty)[/tex]
