Analyze the polynomial function f(x) = 16x-x³. Answer parts (a) through (e). [Hint: First factor the polynomial.] (a) Determine the end behavior of the graph of the function. The graph off behaves like y = for large values of Ix. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Type an integer or a simplified fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) of fis/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The smallest zero is a zero of multiplicity. so the graph of f x= (d) Determine the maximum number of turning points on the graph of the function. The graph of the function will have at most turning points. (e) Use the information in parts (a) through (d) to draw a complete graph of the function. Choose the correct graph below. OA. O B. # the x-axis at x =. The middle zero is a zero of multiplicity. so the graph of f Q A) m Q ос. Q the x-axis at x=. The largest zero is a zero of multiplicity. so the graph of f O D. $ $ the x-axis at
Analyze the polynomial function f(x) = 16x-x³. Answer parts (a) through (e). [Hint: First factor the polynomial.] (a) Determine the end behavior of the graph of the function. The graph off behaves like y = for large values of Ix. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Type an integer or a simplified fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) of fis/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The smallest zero is a zero of multiplicity. so the graph of f x= (d) Determine the maximum number of turning points on the graph of the function. The graph of the function will have at most turning points. (e) Use the information in parts (a) through (d) to draw a complete graph of the function. Choose the correct graph below. OA. O B. # the x-axis at x =. The middle zero is a zero of multiplicity. so the graph of f Q A) m Q ос. Q the x-axis at x=. The largest zero is a zero of multiplicity. so the graph of f O D. $ $ the x-axis at
Chapter5: Polynomial And Rational Functions
Section5.2: Power Functions And Polynomial Functions
Problem 5SE: What can we conclude if, in general, the graph of apolynomial function exhibits the following...
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Analyze the polynomial function f(x) = 16x-x. Answer parts (a) through (e). [Hint: First factor the polynomial.]
(a) Determine the end behavior of the graph of the function.
The graph of f behaves like y =
for large values of Ix.
(b) Find the x- and y-intercepts of the graph of the function.
The x-intercept(s) is/are
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)
The y-intercept is.
(Type an integer or a simplified fraction.)
(c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept.
The zero(s) of f is/are
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)
The smallest zero is a zero of multiplicity, so the graph of f
X =
(d) Determine the maximum number of turning points on the graph of the function.
The graph of the function will have at most turning points.
(e) Use the information in parts (a) through (d) to draw a complete graph of the function. Choose the correct graph below.
O A.
O B.
Ay
the x-axis at x = . The middle zero is a zero of multiplicity
50
A
50
Q
✔
, so the graph of f
O C.
50
the x-axis at x =
The largest zero is a zero of multiplicity
O D.
HALL
50
$
so the graph of f
Q
OU
▼the x-axis at](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbafcd83-01c0-4a70-b139-5a5a0d7792ec%2Faf608251-f641-4f0d-ac2b-27d9466ba58a%2F1dy70dv_processed.png&w=3840&q=75)
Transcribed Image Text:3
Analyze the polynomial function f(x) = 16x-x. Answer parts (a) through (e). [Hint: First factor the polynomial.]
(a) Determine the end behavior of the graph of the function.
The graph of f behaves like y =
for large values of Ix.
(b) Find the x- and y-intercepts of the graph of the function.
The x-intercept(s) is/are
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)
The y-intercept is.
(Type an integer or a simplified fraction.)
(c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept.
The zero(s) of f is/are
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)
The smallest zero is a zero of multiplicity, so the graph of f
X =
(d) Determine the maximum number of turning points on the graph of the function.
The graph of the function will have at most turning points.
(e) Use the information in parts (a) through (d) to draw a complete graph of the function. Choose the correct graph below.
O A.
O B.
Ay
the x-axis at x = . The middle zero is a zero of multiplicity
50
A
50
Q
✔
, so the graph of f
O C.
50
the x-axis at x =
The largest zero is a zero of multiplicity
O D.
HALL
50
$
so the graph of f
Q
OU
▼the x-axis at
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