Question

How do you determine the domain and range of a function?

Answer 1

See below

Explanation:

I will assume `{f(x),x} in RR`

Then, the domain of `f(x)` is the set of all real values of `x` for which `f(x)` is defined. We can think of this as the valid inputs. Let's now call this set `D`

Then the range of `f(x)` is the set of values of `f(x)` over `D`. We can think of this as the valid outputs.

To determine the domain and range of a function, first determine the set of values for which the function is defined and then determine the set of values which result from these.

E.g. `f(x) = sqrtx`

`f(x)` is defined `forall x>=0: f(x) in RR`

Hence, the domain of `f(x)` is `[0,+oo)`

Also, `f(0) = 0` and `f(x)` has no finite upper bound.

Hence, the range of `f(x)` is also `[0,+oo)`

We can deduce these results from the graph of `sqrtx` below.

graph{sqrtx [-4.18, 21.13, -6.51, 6.15]}