Graphs of Polynomial Functions Part 1 Review

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph.

Determine the end behavior of this equation.

f(x) = -x⁵ - 4x +2

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to negative infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to negative infinity.

Answer explanation

Degree: Odd or Even?

Lead Coefficient: Positive or Negative?

Tags

Polynomial End Behavior

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

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to negative infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to negative infinity.

Answer explanation

Degree: Odd or Even?

Lead Coefficient: Positive or Negative?

Tags

Polynomial End Behavior

What is the end behavior for
f(x)= πx⁵-5x²

• A
• B
• C
• D

Answer explanation

Degree: Odd or Even?

Lead Coefficient: Positive or Negative?

Tags

Polynomial End Behavior

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

Answer explanation

Odd Degree: Opposite Direction

Even Degree: Same Direction

(+) LC: Ultimately rises

(-) LC: Ultimately falls

Tags

Polynomial End Behavior

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

Answer explanation

Odd Degree: Opposite Direction

Even Degree: Same Direction

(+) LC: Ultimately rises

(-) LC: Ultimately falls

Tags

Polynomial End Behavior

What is the degree?

• Positive
• Negative
• Odd
• Even

Answer explanation

Odd Degree: Opposite Direction

Even Degree: Same Direction

(+) LC: Ultimately rises

(-) LC: Ultimately falls

Tags

Polynomial End Behavior

What is the leading coefficient?

• Positive
• Negative
• Even
• Odd

Answer explanation

Odd Degree: Opposite Direction

Even Degree: Same Direction

(+) LC: Ultimately rises

(-) LC: Ultimately falls

Tags

Polynomial End Behavior

Is the leading coefficient for the polynomial shown positive or negative?

• Negative

• Positive

• Cannot be determined

Answer explanation

Odd Degree: Opposite Direction

Even Degree: Same Direction

(+) LC: Ultimately rises

(-) LC: Ultimately falls

Tags

Polynomial End Behavior

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

• -∞
  -∞
• +∞
  -∞
• -∞
  +∞
• +∞
  +∞

Answer explanation

x --> -inf: Left

x--> + inf: Right

Tags

Polynomial End Behavior

Which function has this end behavior?

• -x²-3x+1
• -x³+2x²+3
• x⁴+3x³-4x+1
• x⁵-4x⁴+2x²-1

Answer explanation

Odd Degree: Opposite Direction

Even Degree: Same Direction

(+) LC: Ultimately rises

(-) LC: Ultimately falls

Tags

Polynomial End Behavior