The range of aˣ is [tex](0;\ \infty)[/tex].
The range of -aˣ is [tex](-\infty,\ 0)[/tex].
We have [tex]y=-3^x\to-a^x[/tex].
Therefore the range of [tex]g(x)+-3^x[/tex] is [tex](-\infty,\ 0)[/tex].
[tex]f(x)=g(x)+4[/tex] → translate the graph of g(x), 4 units up
Therefore the range of [tex]f(x)=-3^x+4[/tex] is [tex](-\infty,\ 4)[/tex]
