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

1 Answer
May 25, 2018

Answer:

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]}