Recall that:
1) f(x) is an even function if:
[tex]f(-x)=f\mleft(x\mright).[/tex]
2) f(x) is an odd function if:
[tex]f(-x)=-f(x).[/tex]
Now, notice that:
[tex]\begin{gathered} f(-x)=3^{-x}\ne3^x=f(x), \\ f(-x)=3^{-x}\ne-3^x=-f(x). \end{gathered}[/tex]
Therefore f(x)=3^x is neither an even function nor an odd function.
Answer: Neither an even function nor an odd function.
