End Behaviors of Polynomials

Determine the end behavior of the polynomial by identifying the degree and leading coefficient.

f(x) = 5x⁴ - x + 6

• UP-UP

• UP-DOWN

• DOWN-UP

• DOWN-DOWN

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph.  
Enter the polynomial function into a graphing calculator or online graphing tool to determine the end behavior.
f(x) = -x⁵ - 4x +2

• Left up  Right up

• Left up  Right down

• Left down  Right up

• Left down  Right down

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 degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph.
Enter the polynomial function into a graphing calculator or online graphing tool to determine the end behavior.
f(x) = -2x² + 3x

• Left up    Right up

• Left up   Right down

• Left down  Right up

• Left down   Right down

What is the end behavior of this polynomial?

Is the leading coefficient positive or negative? Why?

• The leading coefficient is POSITIVE because the RIGHT SIDE goes UP.

• The leading coefficient is NEGATIVE because the RIGHT SIDE goes UP.

• The leading coefficient is POSITIVE because the RIGHT SIDE goes DOWN.

• The leading coefficient is NEGATIVE because the RIGHT SIDE goes DOWN.

Describe the end behavior of the graph.

• x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

• x → -∞, f(x) → ∞ and x→∞, f(x) →∞

• x → -∞, f(x) → ∞ and x→∞, f(x) → 0

• x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

What is the end behavior of this polynomial?

Describe the end behavior by the degree and leading coefficient.

• The function has an even degree and a positive leading coefficient.

• The function has an even degree and a negative leading coefficient.

• The function has an odd degree and a positive leading coefficient.

• The function has an odd degree and a negative leading coefficient.

What is the end behavior of this graph?

• x → ⁻∞, y→ ⁻∞ and

  x→ ∞, y→ ⁻∞

• x → ⁻∞, y→ ∞ and

  x→ ∞, y→ ∞

• x → ⁻∞, y→ ⁻∞ and

  x→ ∞, y→ ∞

• x → ⁻∞, y→ ∞ and

  x→ ∞, y→ ⁻∞