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

Feb 9, 2018

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

#### Explanation:

Start by changing $y = {2}^{-} x$ to $y = {\left(\frac{1}{2}\right)}^{x}$ to have an untransformed graph.
Here are some characteristics of $y = {\left(\frac{1}{2}\right)}^{x}$ 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 $\frac{1}{2}$ 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.