Question

What is the range of f(x)=-3^x +4

Answer 1

The range of aˣ is
`(0;\ \infty)`.

The range of -aˣ is
`(-\infty,\ 0)`.

We have
`y=-3^x\to-a^x`.

Therefore the range of
`g(x)+-3^x` is
`(-\infty,\ 0)`.

`f(x)=g(x)+4` → translate the graph of g(x), 4 units up

Therefore the range of
`f(x)=-3^x+4` is
`(-\infty,\ 4)`