Let's evaluate every value of the domain into the equation:
so:
[tex]\begin{gathered} x=-2 \\ f(-2)=2^{-2}+4=\frac{1}{2^{^2}}+4=\frac{1}{4}+4=\frac{17}{4}=4.25 \end{gathered}[/tex][tex]\begin{gathered} x=0 \\ f(0)=2^0+4=1+4=5 \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ f(3)=2^3+4=8+4=12 \end{gathered}[/tex]Therefore, the range of the function is:
[tex]R\colon\mleft\lbrace4.25,5,12\mright\rbrace[/tex]