Question

Given the function f(x) = 32 determine the equation of a new function, g(x), that is reflected over the x-axis and then shifted 2 units up.

Answer 1

$f(x)=3^x$

Reflect over the x-axis:

$-f(x)=-3^x$

Shift 2 units up:

$\begin{gathered} g(x)=-f(x)+2=-3^x+2 \\ g(x)=-3^x+2 \end{gathered}$