The domain is the set of values that are allowed to plug into our function and it is represented by the variabel x.. In our case, the domaini s {-1,0,1,2,3}. On the other hand, the range is the set of values that the function assumes after we plug an x value in.
Then, we need to substitute each x value into the given function f(x). So, for x=-1, we have
[tex]\begin{gathered} f(-1)=3(-1)+5 \\ f(-1)=-3+5 \\ f(-1)=2 \end{gathered}[/tex]Similarly, for x=0, we get
[tex]\begin{gathered} f(0)=3(0)+5 \\ f(0)=5 \end{gathered}[/tex]For x=1, we obtain
[tex]\begin{gathered} f(1)=3(1)+5 \\ f(1)=8 \end{gathered}[/tex]Now, for x=2, we have
[tex]\begin{gathered} f(2)=3(2)+5 \\ f(2)=11 \end{gathered}[/tex]and finally, for x=3 we get
[tex]\begin{gathered} f(3)=3(3)+5 \\ f(3)=14 \end{gathered}[/tex]Therefore, the range is the following set:
[tex]{}\lbrace2,5,8,11,14\rbrace[/tex]