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

Question

Isaiah Anthony · Accepted Answer

See below

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]}

Jameson Allen · Answer

undefined To determine the domain of a function, identify all possible input values (x-values) for which the function is defined. To find the range, determine all possible output values (y-values) that the function can produce.