Unit 10.1 - 10.7 - Polynomials and Rationals

What Is the end behavior of this graph?

• lim f(x)→∞ as x→∞
  lim f(x)→−∞ as x→-∞
• lim f(x)→-∞ as x→∞
  lim f(x)→-∞ as x→-∞
• lim f(x)→∞ as x→∞
  lim f(x)→∞ as x→-∞
• lim f(x)→-∞ as x→∞
  lim f(x)→∞ as x→-∞

What Is the end behavior of this graph?

• lim f(x)→∞ as 
  x→∞
  lim f(x)→−∞ as
  x→-∞
• lim f(x)→-∞ as
  x→∞
  lim f(x)→-∞ as
  x→-∞
• lim f(x)→∞ as
  x→∞
  lim f(x)→∞ as
  x→-∞
• lim f(x)→-∞ as
  x→∞
  lim f(x)→∞ as
  x→-∞

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) = -2x² + 3x 

• Left up    Right up
• Left up   Right down
• Left down  Right up
• Left down   Right down

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 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

• A)
• B)

• A)
• B)