Analyze the polynomial function f(x) = (x+7)2 (4-x) using parts (a) through (e). 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 (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) of f 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 lesser zero of the function is of multiplicity, so the graph of f the x-axis at x = (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. O A. O B. Ay 300- Q Q The greater zero of the function is of multiplicity, so the graph of f O C. 300- -300- Q the x-axis at x = O D. 300 -300- Q G
Analyze the polynomial function f(x) = (x+7)2 (4-x) using parts (a) through (e). 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 (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) of f 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 lesser zero of the function is of multiplicity, so the graph of f the x-axis at x = (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. O A. O B. Ay 300- Q Q The greater zero of the function is of multiplicity, so the graph of f O C. 300- -300- Q the x-axis at x = O D. 300 -300- Q G
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 78E
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Transcribed Image Text:Analyze the polynomial function f(x) = (x + 7)² (4− x) using parts (a) through (e).
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) of f 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 lesser zero of the function is of multiplicity, so the graph of f
(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.
O A.
-20
Ay
300-
Q
O B.
-20
Ay
300-
-300-
(...)
the x-axis at x =
Q
. The greater zero of the function is of multiplicity
O C.
-20
Ay
300-
-300
Q
so the graph of f
the x-axis at x =
O D.
-201
Ay
300-
-300
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