Polynomial Characteristics Graphs

What is the absolute minimum point on the polynomial graph?

• There is not an absolute minimum

• (-4,-1.5)

• (-1.5,-4)

• • ∞

Which statements describe the End Behavior of the graph? (Check all that apply)

• x→ -∞, f(x)→ -∞

• x→ -∞, f(x)→∞

• x→ ∞, f(x)→∞

• x→ ∞, f(x)→ -∞

How many of those extrema are maximums?

• 1

• 2

• 3

• 4

How many of the extrema are minimums?

• 1

• 2

• 3

• 4

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

• -∞
  -∞

• +∞
  -∞

• -∞
  +∞

• +∞
  +∞

What type of polynomial could be represented by this graph?

• Even Degree

  - Leading Coefficient

• Even Degree

  + Leading Coefficient

• Odd Degree

  - Leading Coefficient

• Odd Degree

  + Leading Coefficient

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

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

• Left side: Rises  
   Right side: Rises

• Left Side:  Rises
  Right side: Falls

• Left side: Falls
  Right side: Rises

• Left side: Falls
  Right side: Falls

Describe the end behavior of
f(x) = 2x² + 6x⁵ + 10x

• Left side:  Rises
  Right side: Rises

• Left side: Falls
  Right side: Rises

• Left side:Rises
  Right side: Falls

• Left side: Falls
  Right side: Falls

The end behavior of the following is graph is ______________ .

• x → −∞, y → ∞

  x → ∞, y → ∞

• x → −∞, y → - ∞

  x → ∞, y → ∞

• x → −∞, y → - ∞

  x → ∞, y → - ∞

• none of the above