Even Degree Polynomial End Behavior

• Rises on the left and right

• Rises on left, falls on right

• Falls on the left, rises on the right

• Falls on the left and 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 leading coefficient is positive.

• The highest degree is even.

• The leading coefficient is negative.

Describe the end behavior:

Determine the end behavior of the graph of 
f(x) = 3x⁴ + 2x - 5

• As x →∞, f(x) →∞.
  As x→-∞, f(x) →-∞.

• As x →∞, f(x) →∞.
  As x→-∞, f(x) →∞.

• As x →∞, f(x) →-∞.
  As x→-∞, f(x) →∞.

• As x →∞, f(x) →-∞.
  As x→-∞, f(x) →-∞.

Describe the end behavior of the graph.

• x →+∞, y→⁻∞ and x →⁻∞,y→⁻∞

• x →+∞, y→+∞ and x→⁻∞, y→+∞

• x →+∞, y→+∞ and x→⁻∞, y→0

• x →+∞,y→+∞ and x→⁻∞, y→⁻∞

What is the end behavior of even degree polynomial functions?

• The graph is always a parabola

• The ends point in opposite directions

• The graph is always a straight line

• The ends point in the same direction

Describe the end behavior:

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

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Complete the end behavior statement using the degree and leading coefficient: f(x)=-x^7+2x^2+3x-4 . As x→∞, y→ ?