Given: f(x) is an even degree polynomial with a negativeleading coefficient. Ref

Question

Given: f(x) is an even degree polynomial with a negativeleading coefficient. Refer to the given function and answer thefollowing questions. If there is not enough information to answerthe question, write "cannot be determined". a) state the domain of f(x) : I answered (- , )which I believe is correct. b) State the range: c) Where is f(x) continuous? d) True or False? f(x) has an absolute maximum. e) True or False: f(x) does not have any x-intercepts Given: f(x) is an even degree polynomial with a negativeleading coefficient. Refer to the given function and answer thefollowing questions. If there is not enough information to answerthe question, write "cannot be determined". a) state the domain of f(x) : I answered (- , )which I believe is correct. b) State the range: c) Where is f(x) continuous? d) True or False? f(x) has an absolute maximum. e) True or False: f(x) does not have any x-intercepts

Explanation / Answer

recall that all polynomials are continuous everywhere so a) the domain is ( - , ) b) the range cannot be completely determined, see answer to partd c) the function is continuous everywhere , see opening remark d) since the lead coefficient is negative, and thedegree is 4 , for both large negative x and forlarge positive x                     the y value will ultimately be below the x - axis, ,, hencethe the polynomial will have an absolute maxiimum                    and so, the range will not be all of the real numbers e) whether the function has or does not have x - interceptscannot be determined. since we do not know the absolutemaximum. hope this helps

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