Since g(x) is a positive function (the values are positive for all x), the options A. and B. are not correct, because -3^x is a negative number bigger than +2 or -2 for some values of x.
Then, in order to check for C. and D., let's find the value of g(x) in each case for x = 0:
C.
[tex]\begin{gathered} g\mleft(x\mright)=3^{-x}+2 \\ g(0)=3^0+2 \\ g(0)=1+2=3 \end{gathered}[/tex]
D.
[tex]\begin{gathered} g(x)=3^{-x}-2 \\ g(0)=3^0-2 \\ g(0)=1-2=-1 \end{gathered}[/tex]
Looking at the graph, for x = 0 we have g(0) = 3, therefore the correct option is C.
