Question

How do you graph `f(x)=4^(x-2)` and state the domain and range?

Answer 1

domain is `{ x in RR }`
range is `{ y in RR^+ : y != 0 }`

Explanation:

`f(x) = 4^(x-2)` is a continuous function for all `RR`
So domain is `{ x in RR }`

`4^(x-2)` can never equal 0.

If `x >= 2` then `4^(x-2) >= 1`

If `x < 2` then `4^(x - 2)` `= 1/(4^(2 - x)`

As `x -> -oo` then `1/(4^(2 - x)) -> 0`

So range is `{ y in RR^+ : y != 0 }`

`y` axis intercept is `1/16` where `x = 0`

The `x` axis is a horizontal asymptote.

graph{y = 4^(x - 2) [-8.89, 8.885, -4.444, 4.44]}