What is the domain and range of #t^3-t^2+t-1#?

1 Answer
Aug 15, 2017

Answer:

The domain and range are both the whole of the real numbers #RR = (-oo, oo)#

Explanation:

Given:

#f(t) = t^3-t^2+t-1#

The domain of #f(t)# is the set of values of #t# for which it is well defined.

The given #f(t)# is well defined for any value of #t#, so its implicit domain is the whole of the real numbers #RR = (-oo, oo)#.

The range of #f(t)# is the set of values that it can take for some #t# in the domain.

Since #f(t)# is a polynomial of odd degree, its range is the whole of the real numbers #RR = (-oo, oo)#.

Note that as #x->-oo# we find #f(t)->-oo# and as #x->oo# we find #f(t)->oo#. Since #f(t)# is continuous, it takes every value in between #-oo# and #+oo#.

graph{x^3-x^2+x-1 [-10, 10, -5, 5]}