6­1 Extension January 07, 2009
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6­1 Extension January 07, 2009
End Behavior ­ direction of the far left and far right portions of the graph. Four types of end behavior:
up & up
down & down
down & up
up & down
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6­1 Extension January 07, 2009
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6­1 Extension January 07, 2009
Determine the end behavior by looking at the coefficient and degree of the leading term of a polynomial function.
Right:
• If the leading coefficient is positive, then the graph rises to the right.
• If the leading coefficient is negative, then the graph falls to the right.
Left:
• If the degree of the polynomial is even, then the left behavior is the same as the right behavior.
• If the degree of the polynomial is odd, then the left behavior is the opposite of the right behavior.
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6­1 Extension January 07, 2009
Example: Describing End Behavior
Determine the end behavior of the graph of each polynomial.
a. y = 4x3 ­ 3x
The leading coefficient 4 is positive, so the graph rises to the right. b. f﴾x﴿ = ­2x4 + 8x3 ­ 8x2
The degree of the polynomial is 3, which is odd. The left behavior is opposite the right behavior, so the graph falls to the left. The leading coefficient ­2 is negative, so the graph falls to the right. The degree of the polynomial is 4, which is even. The left behavior is the same as the right behavior, so the graph falls to the left. The end behavior is .
The end behavior is .
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6­1 Extension January 07, 2009
Homework: page 312 ﴾1 ­ 10﴿
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