Graph the exponential function $g( x) =\left( \dfrac{1}{2}\!\right) ^{\!\!\!x}.$

Solution We begin by writing $\dfrac{1}{2}$ as $2^{-1}$. Then $$g( x) =\left( \dfrac{1}{2}\!\right) ^{\!\!\!x}=( 2^{-1}) ^{x}=2^{-x}$$

Now we use the graph of $f( x) =2^{x}$ shown in Figure 59 and reflect it about the $y$-axis to obtain the graph $g( x) =2^{-x}.$ See Figure 61.

Figure 61