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Polynomial Graphs

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Key Points End Behavior: what the tails are doing Domain: set of all xs Range: set of all ys Roots/Zeros: where it crosses the x axis Symmetry: even, odd, or neither

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Symmetry Even Symmetric over y axis When you substitute -1 in for x, it doesnt change the sign of each term All even exponents and/or has a constant Odd Symmetric with respect to the origin When you substitute -1 in for x, it changes all of the signs All odd exponents and NO constant Neither Not symmetric about y axis or origin Has a combination of even/odd exponents

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f(x) = -2x 4 + 4x A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior. F. Describe the roots if any.

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f(x) = x 4 - 2x 2 +1 A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior. F. Describe the roots if any.

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f(x) = x 3 - 7x -6 A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior. F. Describe the roots if any.

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f(x) = x 3 – x 2 - 2x A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior. F. Describe the roots if any.

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f(x) = 3x 3 +2x A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior A. List the Domain/Range B. Name the polynomial by degree and number of terms. C. Is it even, odd, or neither? D. Determine the intervals of increase and decrease. E. Describe the end behavior. F. Describe the roots if any.

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