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Writing up end behavior

End Behavior: The left side always starts with "as x→-∞", then look at your graph. If the end heads down, add "y→-∞ ". If the end heads up, add "y→∞". The right side always starts with "as x→∞", then look at your graph. If the end heads down, add "y→-∞ ".If the end heads up, add "y→∞".

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Identifying end behavior from an equation

Words to know:
even degree: The largest exponent the equation has when it is written in standard form is an even number.
odd degree: The largest exponent the equation has when it is written in standard form is an odd number.
Lead coefficient: The coefficient of the term that has the largest exponent when the equation is written in standard form.

Equation Characteristics Example of Equation End Behavior
Even degree, positive lead coefficient f(x)=2x6 – 3x3 – 2x + 7 both ends rise
Even degree, negative lead coefficient f(x)=-3x6 – 3x3 +x - 4 both ends fall
Odd degree, positive lead coefficient f(x)=2x5 – 2x2 + 1 left side falls,right side rises
Odd degree, negative lead coefficient f(x)=-9x3 – 4x2 – 5x left side rises, right side falls