Question

Use the factored form of the polynomial function below to describe its domain andrange.Select one true statement about the domain and one true statement about the range ofthe function.-x²(x − 3)(x + 2)(x - 1) = 0-domain: every polynomial has all real numbers in the domainrange: -2 ≤ x ≤ 3domain: x > 0domain: -2≤ x ≤ 3range: x < 0domain: < 0range: all real numbers because the degree is oddrange: x > 0

Answer 1

Given that

The equation is -x²(x − 3)(x + 2)(x - 1) = 0 and we have to find the correct option for its domain and range.

Explanation -

For the domain,

All the real numbers are the domain for the polynomial.

For the range,

First, we will find the minimum value of the function and then the maximum.

But here the degree of the polynomial is odd.

Degree = Highest power of x = 5

And for the polynomial having an odd degree the range is all the real numbers.

So the range will also be real numbers.

Hence the final answer is options 1 and 7.