End Behavior a x

End Behavior
The parameter a refers to the leading coefficient of a polynomial function of the form
f ( x)  axn  bxn1  cxn2  ...  z
Degree = 1 (Odd)
a>0
a<0
Linear
y
y
x
x
As x   , f ( x)  ______
As x   , f ( x)  ______
As x   , f ( x)  ______
As x   , f ( x)  ______
Degree = 2 (Even)
a>0
a<0
y
Quadratic
y
x
x
As x   , f ( x)  ______
As x   , f ( x)  ______
As x   , f ( x)  ______
As x   , f ( x)  ______
Degree = 3 (Odd)
a>0
a<0
y
Cubic
y
x
As x   , f ( x)  ______
As x   , f ( x)  ______
x
As x   , f ( x)  ______
As x   , f ( x)  ______
Degree = 4 (Even)
a>0
a<0
y
Quartic
y
x
x
As x   , f ( x)  ______
As x   , f ( x)  ______
As x   , f ( x)  ______
As x   , f ( x)  ______
Degree = 5 (Odd)
a>0
a<0
Quintic
y
y
x
As x   , f ( x)  ______
As x   , f ( x)  ______
x
As x   , f ( x)  ______
As x   , f ( x)  ______
Even
Now look at all the functions of even degree. What do you notice about their end behavior? What
about the end behavior of odd functions?
Degree = 2n (Even)
a>0
As x   , f ( x)  ______
As x   , f ( x)  ______
a<0
As x   , f ( x)  ______
As x   , f ( x)  ______
Odd
Degree = 2n + 1 (Odd)
a>0
As x   , f ( x)  ______
As x   , f ( x)  ______
a<0
As x   , f ( x)  ______
As x   , f ( x)  ______