Polynomials - Even and Odd Functions

What is the end behavior as x → -∞ f(x)→ ?

• -∞

• ∞

How many relative extrema(tuning points) are in the picture?

• 2

• 3

• 4

• 5

What is the predicted end behavior of: y=-2x⁴+3x-1

• up on both ends

• down on both ends

• up on left, down on right

• down on left, up on right

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even

• Leading Coefficient Positive
  Degree - Odd

• Leading Coefficient Negative
  Degree - Even

• Leading Coefficient Negative
  Degree - Odd

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even

• Leading Coefficient Positive
  Degree - Odd

• Leading Coefficient Negative
  Degree - Even

• Leading Coefficient Negative
  Degree - Odd

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even

• Leading Coefficient Positive
  Degree - Odd

• Leading Coefficient Negative
  Degree - Even

• Leading Coefficient Negative
  Degree - Odd

Identify the zeros:

• x=-2, x=-1, x=0

• x=-2, x=0

• x=-1, x=0, x=2

• x=-2, x=0, x=1

Match the graph to the function

• f(x) = -2x⁶+9x²

• f(x) = x⁴+x³-5x²-6

• f(x) = -½x⁴+1

• f(x) = -x²+3x

How many real solutions does the function have?

• 0

• 1

• 2

• 3

Using the degree and leading coefficient, match the graph to an equation.

• y=-(x-1)²(x+2)²

• y=(x-1)²(x+2)²

• y=(x-1)(x+2)²

• y=-(x-1)²(x+2)²