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

Apr 24, 2017

Note that:

$g \left(x\right) = 5 - {2}^{x} = \left(- {2}^{x}\right) + 5 = f \left(x\right) + 5$

So the graph of $g \left(x\right)$ is identical to the graph of $f \left(x\right)$, but $5$ greater.

Take $f \left(x\right)$:

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]}