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Explain how to determine the end behavior of a polynomial.

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You look at what the polynomial y values are for x going toward + infinity (positive large) and - infinity (negative large). Since we are talking about polynomials, it is sufficient to just look at the "x" term that has the largest exponent. If that exponent is even, then at x large positive and x large negative, the y will go to y large positive if the coefficient is positive. If the coefficient is negative, then the y will go to y large negative.
If the exponent is odd, then the end behavior will be going to y large negative for one side and y large positive for the other side, depending again on the coefficient, whether it is negative or positive.
So, if you have an odd exponent for the largest exponent and a positive coefficient, the y will go toward positive infinity on the right and negative infinity on the left. Just the opposite for a negative coefficient.

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