SOLUTION: Determine the right-hand and left-hand end behavior of the polynomial function, f(x)=114+6x-x^2-x^5. (1)rises to the left and to the right. (2) falls to the left and to the right.

Question 202603: Determine the right-hand and left-hand end behavior of the polynomial function, f(x)=114+6x-x^2-x^5. (1)rises to the left and to the right. (2) falls to the left and to the right. (3) rises to the left and falls to the right. (4) rises to the right and falls to the left. UGH! PLEASE HELP.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The high order term is

. Clearly, as the magnitude of

gets larger, this term will take over and the other terms won't matter that much. Any time you raise a negative number to an odd power, the result is negative, and since the coefficient is negative, the overall result for negative values of

is that the high-order term will be positive. So the graph clearly rises on the left. Likewise, for positive values of

the value of

will be positive and the negative coefficient makes the value of that term negative, hence the graph will fall on the right.

John

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