Question

How do you graph `f(x)=(3/2)^x-2` and state the domain and range?

Answer 1

Domain: `(-oo,+oo)`
Range: `(-2,+oo)`

Explanation:

`f(x) = (3/2)^x-2`

`f(x)` is the exponential increasing graph of `y=(3/2)^x` transformed ("shifted") by 2 units negative ("down") on the `y-`axis.

`f(x)` is defined `forall x in RR`

Hence, the domain of `f(x)` is `(-oo,+oo)`

Consider, `lim_(x->-oo) f(x) =-2`

also, `f(x)` has no finite upper bound.

Hence, the range of `f(x)` is `(-2, +oo)`

We can deduce these results from the graph of `f(x)` below.

graph{(3/2)^x -2 [-10, 10, -5, 5]}