Analyze the polynomial function f(x) = x²(x + 2) using parts (a) through (e). www (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. (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 at x = the x-axis at x = the x-axis The greater zero of the function is of multiplicity, so the graph of f 0.
Analyze the polynomial function f(x) = x²(x + 2) using parts (a) through (e). www (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. (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 at x = the x-axis at x = the x-axis The greater zero of the function is of multiplicity, so the graph of f 0.
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
Section4.2: Polynomial Functions
Problem 82E
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Question
analyze the polynomial function
Transcribed Image Text:←
Analyze the polynomial function f(x) = x²(x + 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 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
at x =
O A.
The greater 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.
the x-axis
B.
D.
Ау
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