AC Geo/Adv. A U6 Worksheet 10

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.
Ex5) ( )
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.
a)
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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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a)
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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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3)
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4)
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Max # x-intercepts ____
Max # x-intercepts ____
Max # turning points ____
Max # turning points ____
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5)
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6)
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Max # x-intercepts ____
Max # x-intercepts ____
Max # turning points ____
Max # turning points ____
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7)
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8)
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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.
9)
10)
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Degree _____
L.C. ______
Degree _____
L.C. ______
11)
12)
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Degree _____
L.C. ______
Degree _____
L.C. ______
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.
13)
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15)
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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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