Find the domain, range and roots (that is, where y=0) of the function

y = -x^3+x^2+x-1

Please show your working. Thankyou <3!

Domain is all real numbers and so is the range. Certainly x = 1 is a root. x= -1 is also a root. The function factors as -(x-1)^2*(x+1).

This is a polynomial . All polynomials have domain all real x.

This is an odd degree polynomial. Therefore the range is all real y.

You might guess that 1 is a root. Then divide by (x-1). You are left with -x^2 + 1, which factors as -(x+1)(x-1).