Graphing an Exponential Function

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.