## Precalculus (6th Edition) Blitzer

$g(x)=4^{-x}$
The graph of $f(x)=b^{x}$, when $b\gt 1$, has the following characteristics: - it is above the x-axis at all times, always rising, - on the far left, it nears, but never touches the x-axis, - it rises to cross the y-axis at the point (0,1) - it rises to pass through the point (1,b), - and keeps rising... The graph (4) corresponds to this description, and it is the graph of $f(x)=4^{x}.$ We obtain this graph (graph 1) from graph 4 by reflecting it across the y-axis, so this is the graph of $f(-x)=4^{-x}=g(x).$ Answer: $g(x)=4^{-x}$