Question

Graph the exponential functionula1" title=" f(x)=\frac{1}{2}^{x} " alt=" f(x)=\frac{1}{2}^{x} " align="absmiddle" class="latex-formula"> .

Answer 1

$f(x)=\left(\dfrac{1}{2}\right)^x\\\\for\ x=-3\to y=\left(\dfrac{1}{2}\right)^{-3}=2^3=8\to(-3,\ 8)\\\\for\ x=-2\to y=\left(\dfrac{1}{2}\right)^{-2}=2^2=4\to(-2,\ 4)\\\\for\ x=-1\to y=\left(\dfrac{1}{2}\right)^{-1}=2^1=2\to(-1,\ 2)\\\\for\ x=0\to y=\left(\dfrac{1}{2}\right)^0=1\to(0,\ 1)\\\\for\ x=1\to y=\left(\dfrac{1}{2}\right)^1=\dfrac{1}{2}\to\left(1,\ \dfrac{1}{2}\right)\\\\for\ x=2\to y=\left(\dfrac{1}{2}\right)^2=\dfrac{1}{4}$