Question

How do you use the graph of `f(x)=-2^x` to describe the transformation of `g(x)=5-2^x`?

Answer 1

Note that:

`g(x)=5-2^x=(-2^x)+5=f(x)+5`

So the graph of `g(x)` is identical to the graph of `f(x)`, but `5` greater.

Take `f(x)`:

graph{-2^x [-14.24, 14.24, -7.12, 7.12]}

And shift the graph up `5` units:

graph{5-2^x [-16.01, 16.04, -8.01, 8.01]}