Mathematical Modeling: Part Three — Test

Question 1 • Mathematics III

What are the domain and range of the function f of x is equal to 1 fourth times open paren x cubed plus 6 x squared plus 5 x minus 4 close paren ?

Answer

domain: open paren negative infinity comma infinity close paren range: open paren negative infinity comma infinity close paren

domain: open paren negative 6 point 5 comma 2 point 5 close paren range: open paren negative infinity comma infinity close paren

domain: open paren negative infinity comma 1 fourth close paren range: open paren negative 4 comma infinity close paren

domain: open paren negative infinity comma infinity close paren range: open paren negative 1 point 3 comma 2 point 3 close paren

Explanation

The function is a cubic polynomial multiplied by 1/4. Polynomials are defined for every real number, so the domain is (−∞, ∞). Since this is a cubic with a nonzero leading coefficient, its values extend without bound in both directions, giving the range (−∞, ∞). Therefore, choice B is correct.

AI-written and checked against the verified answer.

More from this Course

Test

Test

Test