Answer
$g(x)=4^{-x}$
Work Step by Step
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: $g(x)=4^{-x}$
