Analyze the polynomial function f(x) = (x+7)(x-4)² using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = for large values of Ixl. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Simplify your answer. Type an integer or a 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) off is/are[ (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The smaller zero of the function is of multiplicity. so the graph of f the x-axis at x =. The larger zero of the function is of multiplicity. so the graph of f the x-axis at x=
Analyze the polynomial function f(x) = (x+7)(x-4)² using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = for large values of Ixl. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Simplify your answer. Type an integer or a 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) off is/are[ (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The smaller zero of the function is of multiplicity. so the graph of f the x-axis at x =. The larger zero of the function is of multiplicity. so the graph of f the x-axis at x=
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
Problem 80E
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![Analyze the polynomial function f(x) = (x + 7)(x-4)² using parts (a) through (e).
(a) Determine the end behavior of the graph of the function.
The graph of f behaves like y = for large values of [x].
(b) Find the x- and y-intercepts of the graph of the function.
The x-intercept(s) is/are
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The y-intercept is
(Simplify your answer. Type an integer or a 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) off is/are
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The smaller zero of the function is of multiplicity , so the graph of f
O A.
(d) Determine the maximum number of turning points on the graph of the function.
(Type a whole number.)
(e) Use the above information to draw a complete graph of the function. Choose the correct graph below.
300
-300
A)
Q
O B.
the x-axis at x =
300
C
Q
. The larger zero of the function is of multiplicity, so the graph of f
O C.
300
Q
the x-axis at x =
O D.
300
-300-
Q](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56dda719-03db-48ea-b20a-1a92b437a8a1%2F8c039913-548c-488d-8e23-d4e997857442%2Filgqxu8_processed.png&w=3840&q=75)
Transcribed Image Text:Analyze the polynomial function f(x) = (x + 7)(x-4)² using parts (a) through (e).
(a) Determine the end behavior of the graph of the function.
The graph of f behaves like y = for large values of [x].
(b) Find the x- and y-intercepts of the graph of the function.
The x-intercept(s) is/are
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The y-intercept is
(Simplify your answer. Type an integer or a 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) off is/are
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The smaller zero of the function is of multiplicity , so the graph of f
O A.
(d) Determine the maximum number of turning points on the graph of the function.
(Type a whole number.)
(e) Use the above information to draw a complete graph of the function. Choose the correct graph below.
300
-300
A)
Q
O B.
the x-axis at x =
300
C
Q
. The larger zero of the function is of multiplicity, so the graph of f
O C.
300
Q
the x-axis at x =
O D.
300
-300-
Q
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