(a) Determine the end benavior 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 real 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. Touch al спо 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.) so the graph of f Starting from least to greatest, the first zero of the function is of multiplicity of multiplicity so the graph of f the x-axis at x = . The third zero of the function is of multiplicity =. The fourth zero of the function is of multiplicity, so the graph of f he x-axis at x = (= the x-axis at x = The second zero of th , so the graph off the x-
(a) Determine the end benavior 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 real 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. Touch al спо 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.) so the graph of f Starting from least to greatest, the first zero of the function is of multiplicity of multiplicity so the graph of f the x-axis at x = . The third zero of the function is of multiplicity =. The fourth zero of the function is of multiplicity, so the graph of f he x-axis at x = (= the x-axis at x = The second zero of th , so the graph off the 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 81E
Related questions
Question
Transcribed Image Text:Analyze the polynomial function f(x) = 2x (x² − 4) (x + 4) using parts (a) through (e).
(a) Determine the end benavior 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 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
(c) Determine the real 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 comma to separate answers as needed. Type each answer only once.)
Starting from least to greatest, the first zero of the function is of multiplicity
of multiplicity so the graph of f
The fourth zero of the function is of multiplicity
X=
Touch or
cross?
so the graph of f
the x-axis at x = The third zero of the function is of multiplicity
so the graph of f
▼he x-axis at x =
the x-axis at x = The second zero of the function is
▼the x-axis at
so the graph off
Transcribed Image Text:(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.
A.
Ау
300
♫
B.
300
Ау
Q
G
O C.
Ay
O D.
300
Ay
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