Polynomial End Behavior Slides

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→⁻∞

Tags

CCSS.HSF-IF.C.7A

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) = 2x³ - x + 5

• Left up    Right up

• Left up   Right down

• Left down   Right up

• Left down   Right 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

• 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

• 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

• 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

Is the degree of the graphed polynomial even or odd?

• Odd

• Even

Using the graph, what can we assume about the equation?

• Degree - Even

  Leading Coefficient - Positive

• Degree - Odd

  Leading Coefficient - Positive

• Degree - Even

  Leading Coefficient - Negative

• Degree - Odd

  Leading Coefficient - Negative

Using the graph, what can we assume about the equation?

• Degree - Even

  Leading Coefficient - Positive

• Degree - Odd

  Leading Coefficient - Positive

• Degree - Even

  Leading Coefficient - Negative

• Degree - Odd

  Leading Coefficient - Negative