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Polynomial Graphs

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**Key Points End Behavior: what the “tails” are doing**

Domain: set of all x’s Range: set of all y’s Roots/Zeros: where it crosses the x axis Symmetry: even, odd, or neither

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**Symmetry Even Odd Neither Symmetric over y axis**

When you substitute -1 in for x, it doesn’t 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) = -2x4 + 4x2 - 2 List the Domain/Range**

Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior. Describe the roots if any.

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**f(x) = x4 - 2x2 +1 List the Domain/Range**

Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior. Describe the roots if any. List the Domain/Range Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior

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**f(x) = x3 - 7x -6 List the Domain/Range**

Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior. Describe the roots if any. List the Domain/Range Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior

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**f(x) = x3 – x2 - 2x List the Domain/Range**

Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior. Describe the roots if any. List the Domain/Range Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior

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**f(x) = 3x3 +2x List the Domain/Range**

Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior. Describe the roots if any. List the Domain/Range Name the polynomial by degree and number of terms. Is it even, odd, or neither? Determine the intervals of increase and decrease. Describe the end behavior

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The first column shows a sequence of numbers. Second column shows the first difference. (-6) – (-4) = -2 If the pattern continues, what is the 8 th number.

The first column shows a sequence of numbers. Second column shows the first difference. (-6) – (-4) = -2 If the pattern continues, what is the 8 th number.

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