Question

How do you graph `y=(0.5)^x` and state the domain and range?

Answer 1

graph{(0.5)^x [-10, 10, -5, 5]}

domain: `(-oo,oo)`
range: `(0, oo)`

Explanation:

`y = (0.5)^x`

domain (the values that `x` could take):

`x` could be substituted for all real numbers, including `pi` and `e`.

this means that the values that `x` could take go from `-oo` to `oo`.

`therefore -oo` and `oo` are the domain, and are written as `(-oo,oo)`

range (the values that `y` could take):

`y = (0.5)^x`

the roots (square, cube, etc.) of negative numbers are lateral (`i` or a factor/multiple of this), and 0.5 is a real number-

`therefore (0.5)^x >0`.

since the value of `(0.5)^x` decreases as `x` increases, `y` gradually goes towards `0`.

although it does not actually reach `0`, `0` is its limit as `x` approaches `oo`.

this means that the values `y` could take go from `0` to `oo`.

`therefore 0` and `oo` are the range, and are written as `(0, oo)`.