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

1 Answer
May 25, 2018

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]}