Question

How do you graph `y=2^-x`?

Answer 1

here is the graph
graph{2^-x [-10, 10, -5, 5]}

Explanation:

Start by changing `y=2^-x` to `y=(1/2)^x` to have an untransformed graph.
Here are some characteristics of `y=(1/2)^x` to make sure you plot the points correctly:

-it will have y-intercept (0,1)

-the domain is all reals

-has `0<`base`<1`

-is a decreasing function

-the horizontal asymptote is `y=0`, therefore the range is `y>0`

To graph, start with the point (0,1) and multiply `y` by `1/2` to get the positive coordinates of `x`. To get the negative coordinates of `x`, start with (0,1) and multiply `y` by 2. Keep in mind the restrictions and guidelines above.

then graph accordingly making sure to get close to zero, but never actually reach it.