www.iTutoring.com -­‐ NOTES Name _________________________________ End Behavior of Polynomials Date ___________________ Period _______ The behavior of the graph of f(x) as x approaches positive infinity or negative infinity
x ! -∞
x!∞
“as x approaches negative infinity”
“as x approaches positive infinity”
f(x) ! -∞ as x ! -∞
y
f(x) ! ∞ as x ! ∞
∞
f(x)
-∞ " x
x!∞ x
-∞
Determine the end behavior of the following functions
y
y
x
f(x)
g(x)
x
f(x) ! ____ as x ! ∞
g(x) ! ____ as x ! ∞
f(x) ! ____ as x ! -∞
g(x) ! ____ as x ! -∞
Given the equation of a polynomial function,
we can analyze the degree and leading coefficient of the polynomial.
f(x) ! ∞ as x ! -∞
f(x) ! -∞ as x ! ∞
f(x) ! -∞ as x ! -∞
Negative
f(x) ! ∞ as x ! ∞
Positive
Even Degree
Odd Degree
f(x) ! ∞ as x ! ∞
f(x) ! -∞ as x ! -∞
f(x) = x2
f(x) = x3
f(x) ! -∞ as x ! ∞
f(x) ! ∞ as x ! -∞
f(x) =
f(x) =
-x2
-x3
Determine the end behavior of the
following functions
Positive
Negative
f(x) = 2x5 + 8x2 + 7x
Even Degree
Odd Degree
f(x) = x2
f(x) = x3
f(x) = -x2
f(x) = -x3
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End Behavior of Polynomials Pg. 2 Determine the end behavior of the
following functions
Positive
Negative
f(x) = -4x6 – 5x3 + 10
Even Degree
Odd Degree
f(x) = x2
f(x) = x3
f(x) = -x2
f(x) = -x3
Determine the end behavior of the
following functions
Positive
Negative
f(x) = 5x4 – x3 + 5x2 – 2x + 12
Even Degree
Odd Degree
f(x) = x2
f(x) = x3
f(x) = -x2
f(x) = -x3
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End Behavior of Polynomials Pg. 3 Determine the end behavior of the
following functions
Positive
Negative
f(x) = -2x7 – 4x5 + x3 + 10x + 9
Even Degree
Odd Degree
f(x) = x2
f(x) = x3
f(x) = -x2
f(x) = -x3
Determine if the degree of the following
function is even or odd and if the leading
coefficient is positive or negative.
f(x)
Negative
Positive
Even Degree
Odd Degree
f(x) = x2
f(x) = x3
f(x) = -x2
f(x) = -x3
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End Behavior of Polynomials Pg. 4 Determine if the degree of the following
function is even or odd and if the leading
coefficient is positive or negative.
Positive
Negative
f(x)
Even Degree
Odd Degree
f(x) = x2
f(x) = x3
f(x) = -x2
f(x) = -x3
Determine if the degree of the following
function is even or odd and if the leading
coefficient is positive or negative.
Positive
Negative
f(x)
Even Degree
Odd Degree
f(x) = x2
f(x) = x3
f(x) = -x2
f(x) = -x3
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End Behavior of Polynomials Pg. 5 Determine if the degree of the following
function is even or odd and if the leading
coefficient is positive or negative.
Positive
Negative
f(x)
Even Degree
Odd Degree
f(x) = x2
f(x) = x3
f(x) = -x2
f(x) = -x3
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End Behavior of Polynomials Pg. 6