SOLUTION: What is the appropriate domain and range of this cubic function in interval notation: {{{y=x^3+2x^2-3x}}}

Algebra ->  Functions -> SOLUTION: What is the appropriate domain and range of this cubic function in interval notation: {{{y=x^3+2x^2-3x}}}      Log On


   

Question 172197: What is the appropriate domain and range of this cubic function in interval notation: y=x%5E3%2B2x%5E2-3x
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
What is the appropriate domain and range of this cubic function in interval notation: y=x%5E3%2B2x%5E2-3x

Every cubic polynomial functon of odd degree has the 
same domain and range, namely "all real numbers".

Since this is third degree polynomial, and 3 is odd,
then its domain in interval notation is

matrix%281%2C5%2C++%22%28%22%2C++-infinity%2C++%22%2C%22%2C+infinity%2C++%22%29%22%29

and the range in interval notation is also

matrix%281%2C5%2C++%22%28%22%2C++-infinity%2C++%22%2C%22%2C+infinity%2C++%22%29%22%29.

[Even degree polynomials have that same domain, but not
the same range, as odd-degree polynomials do.]

Edwin