The basic way to graph any function y= f(x) is to calculate a few coordinate pairs: \(\displaystyle (x_0, y_0)= (x_0, f(x_0))\), plot those points a draw a curve through them. For \(\displaystyle y= 2^x\) they might be \(\displaystyle (0, 2^0)= (0, 1)\), \(\displaystyle (1, 2^1)= (1, 2)\), \(\displaystyle (2, 2^2)= (2, 4)\), \(\displaystyle (-1, 2^{-1})= (-1, 1/2)\), \(\displaystyle (-2, 2^{-2})= (-2, 1/4)\). For \(\displaystyle y= (1/3)^x\) they might be \(\displaystyle (0, (1/3)^0)= (0, 1)\), \(\displaystyle (1, (1/3)^1)= (1, 1/3)\), \(\displaystyle (2, (1/3)^2)= (2, 1/9)\), \(\displaystyle (-1, (1/3)^{-1})= (-1, 3)\), \(\displaystyle (-2, (1/3)^{-2})= (-2, 9)\).
You say
"labeling
1. at least 2 coordinates on each side of the y axis.
2. the asymptote."
"On each side of the y axis" means some negative and some positive x values, But "2" makes no sense. neither graph has an "asymptote".