SOLUTION: What is the domain and range of the function g(x)= x^4-3x^3+2x^2+x-1 I had gotten a domain of all real numbers, and I had estimated the range to include all numbers from [-1

Question 572760: What is the domain and range of the function g(x)= x^4-3x^3+2x^2+x-1
I had gotten a domain of all real numbers, and I had estimated the range to include all numbers from [-1, infinity), but I was told the range is incorrect.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You're almost correct.
has a double zero at , which are zeros of .
It changes sign at , approximately -0.62 and 1.62, and is negative only in between those irrational zeros, but touches zero at in between.
is close enough to the absolute minimum of the function, but so close to zero is a good approximation, and since
and , -1.1 may be a better estimate of the minimum.
With a calculator, or computer you could estimate it even closer.
I you were taught about derivatives of polynomial functions, you could exactly locate and calculate the minimum.
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