Polynomial Function (End Behavior, Turning Points and Classification)

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

• -∞
  -∞

• +∞
  -∞

• -∞
  +∞

• +∞
  +∞

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) → ∞

Which function has this end behavior?

• -1x⁴-3x³+3

• -2x⁷+2x⁴+4

• 3x⁸+3x⁵-4x+7

• 4x⁵-4x⁴+2x³-9

Which function has this end behavior?

• -x²-3x+1

• -x³+2x²+3

• x⁴+3x³-4x+1

• x⁵-4x⁴+2x²-1

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

• 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) →-∞.

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

• 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) → -∞.

Match the following graph with an equation that has the same End Behaviors.

• 
• 
• 
• 

Identify the degree of the polynomial and the sign of the leading coefficient based on the end behavior of the polynomial.

• Positive

• Even

• Negative

• Odd

• Increasing

• Decreasing

• 0

• 1

• 2

• 3