Question

Which of the following is a point on the graph of y=(1/2)^x?

Answer 1

The third option is the answer

Answer 2

$\bf 1.~(0,0)~\hspace{5em}0=\left( \cfrac{1}{2} \right)^0\implies 0\ne 1\qquad \otimes \\\\\\ 2.~\left( 0,\frac{1}{2} \right)~\hspace{5em}\cfrac{1}{2}=\left( \cfrac{1}{2} \right)^0\implies \cfrac{1}{2}\ne 1\qquad \otimes$

$\bf 4.~(2,1)~\hspace{5em}1=\left( \cfrac{1}{2} \right)^2\implies 1=\cfrac{1^2}{2^2}\implies 1\ne \cfrac{1}{4}\qquad \otimes \\\\\\ 3.~\left(2,\frac{1}{4} \right)~\hspace{5em}\cfrac{1}{4}=\left( \cfrac{1}{2} \right)^2\implies \cfrac{1}{4}=\cfrac{1^2}{2^2}\implies \cfrac{1}{4}=\cfrac{1}{4}\qquad \checkmark$