Question

How do you graph `y=(1/2)^x` using a table of values?

Answer 1

Take some `(x,y)` samples and connect them.

Explanation:

Unfortunately, we can draw exact graph of very few functions. Table of values can help drawing every (other) function, but you will never reach `100%` accuracy, since you can't tell what happens in the middle of your samples.

Anyway, it's pretty straightforward: you just choose a bunch of `x` values, and compute their images `y`, using the rule described by the function.

In your case, we may restyle the function a little bit by writing

`(1/2)^x = 1/2^x`

and thus, for example, if we choose the `x` values `-3,-2,-1,0,1,2,3` we have corresponding values

`-3\to1/2^(-3)=8`
`-2\to1/2^(-2)=4`
`-1\to1/2^(-1)=2`
`0\to1/2^0=1/1=1`
`1\to1/2^1=1/2`
`2\to1/2^2=1/4`
`3\to1/2^3=1/8`

Plot all the `(x,y)` couples you got and try to sketch the rest of the function accordingly