1. Polynomial Graphs

2. 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

3. 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

4. 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.

5. 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

6. 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

7. 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

8. 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