Question 978157
"Find the range."
g(x) is a polynomial function.  Range will be all real numbers and also domain is all real numbers.


You could try derivative to help find minimum  (or maximum) y values.  


{{{dg/dx=4x^3-9x^2+4x+1}}}.
Where is this equal to 0?   (they may be real, but not rational.)


There is a MAXIMUM (local) for x=1.  Try then using this root to decompose 4x^3-9x^2+4x+1 into factors.