Question

Find the domain of the function. (enter your answer using interval notation.) f(x) = 3x3 − 1 x2 + 2x − 15

Answer 1

Hello!

A cubic function is in the form of $f(x)=ax^{3}+bx^{2}+cx+d$.

All cubic functions have a domain of all real numbers, the range also has a range of all real numbers.

Interval notation is used for representing a function/interval as a pair of numbers. Parentheses and brackets are used to show if the endpoints of a given function/interval are included or excluded. Brackets allow the endpoints to be included while parentheses exclude the endpoint.

Our first instinct would be that the domain is written as [-∞, ∞], but that is incorrect. Infinity is not a number, but it is a concept. This means that they are excluded from the domain.

Therefore, the domain of the function f(x) is (-∞, ∞).