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AC Geo/Adv. A
U6 Worksheet 10
Name_________________________
END BEHAVIOR OF POLYNOMIAL FUNCTIONS
Odd degreed functions with a positive leading coefficient
The function approaches negative infinity as x approaches negative infinity and the
function approaches positive infinity as x approaches positive infinity
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Odd degreed functions with a negative leading coefficient
The function approaches positive infinity as x approaches negative infinity and the function
approaches negative infinity as x approaches positive infinity
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Even degreed functions with a positive leading coefficient
The function approaches positive infinity as x approaches negative infinity and the function
approaches positive infinity as x approaches positive infinity
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Even degreed functions with a negative leading coefficient
The function approaches negative infinity as x approaches negative infinity and the
function approaches negative infinity as x approaches positive infinity
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Describe the end behavior of the graph of the polynomial function by completing the
statements.
Ex1)
Ex3)
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Ex2)
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Ex4)
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The maximum number of turning points is equal to 1 less than the degree of the
polynomial.
State the degree of the polynomial and the maximum number of turning points of its
graph.
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Ex6)
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Ex7) ( )
When you graph a polynomial, the roots of the polynomial are the points where the
curved formed by the polynomial cuts the x-axis (the x-intercepts).
Ex8) Find the roots of the polynomial
a) y = x2 + 14x – 15
b) y= x2 – 25
c) y = x4 +7x3 – 18x2
The multiplicity of a root is the number of times a given polynomial equation has a
value as a root. For the polynomial equation ( )
, k is a repeated solution, or a root
with a multiplicity greater than 1, if and only if the factor x – k has an exponent greater
than 1 when f(x) is factored completely.
If the exponent is odd, the graph of f crosses the x-axis at the zero
If the exponent is even, the graph of f touches the x-axis at the zero
Ex9) Find all of the zeros of the function. Then determine the multiplicity of each zero
and the maximum number of turning points of the graph.
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Ex10) Make a rough sketch of the graph using end behavior, zeros, and multiplicity to
make it as accurate as possible.
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Complete the statements to describe the end behavior, the maximum number of xintercepts, and the number of turning points of the graphs of the following
polynomial functions.
1)
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2)
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____ as
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Max # x-intercepts ____
Max # x-intercepts ____
Max # turning points ____
Max # turning points ____
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Max # x-intercepts ____
Max # x-intercepts ____
Max # turning points ____
Max # turning points ____
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Max # x-intercepts ____
Max # x-intercepts ____
Max # turning points ____
Max # turning points ____
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Max # x-intercepts ____
Max # x-intercepts ____
Max # turning points ____
Max # turning points ____
Describe the end behavior of the graph. Then describe the degree and leading
coefficient of the polynomial function.
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Degree _____
L.C. ______
Degree _____
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Degree _____
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Degree _____
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Find all of the zeros of the function. Then determine the multiplicity of each zero
and the exact number of turning points of the graph.
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Make a rough sketch of the graph using end behavior, zeros, and multiplicity to
make it as accurate as possible.
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