Polynomial Graphs

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

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

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.

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

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

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

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