How to Determine the End Behaviour of a Polynomial Function

How to Determine the End Behaviour of a Polynomial Function

1. ODD NUMBER: This means the function is an Odd-Degree Polynomial (ex. 2x + 3x + 4x +5)

   • Is the leading coefficient (leading term) a positive or negative number?
     • Positive [a > 0]
       • End Behaviour: as x→ -∞, y→ -∞ as x→ ∞, y→ ∞
         • Example:
           • Domain= {x Range= {y
             • Max/Min: Neither positive or negative have a maximum or minimum value
               • Turning Points: Even number (The largest number of turning points is n-1, if n= degree)
         • The function starts in the 3rd quadrant and ends in the 1st quadrant
     • Negative [a < 0]
       • End Behaviour: as x→ -∞, y→ ∞ as x→ ∞, y→ -∞
         • Example:
           • Domain= {x Range= {y
         • The function starts in the 2nd quadrant and ends in the 4th quadrant

2. EVEN NUMBER: This means the function is an Even-Degree Polynomial (ex. 3x + 4x +5)

   • Is the leading coefficient (leading term) a positive or negative number?
     • Positive [a > 0]
       • End Behaviour: as x→ -∞, y→ ∞ as x→ ∞, y→ ∞
         • Example:
           • Domain= {x Range= {y|y > a}
             • Max/Min: Minimum value→a
         • The function starts in the 2nd quadrant and ends in the 1st quadrant
     • Negative [a < 0]
       • End Behaviour: as x→ -∞, y→ -∞ as x→ ∞, y→ -∞
         • Example:
           • Domain= {x Range= {y|y < a}
             • Max/Min: Maximum value→a
               • Turning Points: Odd number (The largest number of turning points is n-1, if n= degree)
         • The function starts in the 3rd quadrant and ends in the 4th quadrant

3. Is the largest degree of the Polynomial function an Odd or Even number?

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