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

1 Answer
George C.
Aug 15, 2017

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]}

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