Analyze the polynomial function f(x) = 5x (x - 4) (x + 3) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = 5x for large values of |x|. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are 0,2, – 2, – 3. (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 0. (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. The zero(s) of f islare 0, - 2,2, – 3. (Simplify your answer. Type an integer or a fraction. Use a 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 1, so the graph of f crosses the x-axis at x= 0. The second zero of the function is of multiplicity 1, so the graph of f crosses the x-axis at x = 2. The third zero of the function is of multiplicity 1, so the graph of f crosses the x-axis at x = - 2. The fourth zero of the function is of multiplicity 1, so the graph of f crosses the x-axis at x = - 3
Analyze the polynomial function f(x) = 5x (x - 4) (x + 3) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = 5x for large values of |x|. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are 0,2, – 2, – 3. (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 0. (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. The zero(s) of f islare 0, - 2,2, – 3. (Simplify your answer. Type an integer or a fraction. Use a 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 1, so the graph of f crosses the x-axis at x= 0. The second zero of the function is of multiplicity 1, so the graph of f crosses the x-axis at x = 2. The third zero of the function is of multiplicity 1, so the graph of f crosses the x-axis at x = - 2. The fourth zero of the function is of multiplicity 1, so the graph of f crosses the x-axis at x = - 3
Chapter3: Polynomial Functions
Section: Chapter Questions
Problem 38RE: Finding Real Zeros of a Polynomial Function In Exercises 37-42, (a) find all real zeros of the...
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Transcribed Image Text:Analyze the polynomial function f(x) = 5x (x - 4) (x + 3) using parts (a) through (e).
(a) Determine the end behavior of the graph of the function.
The graph of f behaves like y = 5x for large values of |x|.
(b) Find the x- and y-intercepts of the graph of the function.
The x-intercept(s) is/are 0,2, – 2, – 3.
(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 0.
(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.
The zero(s) of f islare 0, - 2,2, – 3.
(Simplify your answer. Type an integer or a fraction. Use a 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 1, so the graph of f crosses the x-axis at
x= 0. The second zero of the function is of multiplicity 1, so the graph of f crosses the x-axis at x = 2. The third zero of
the function is of multiplicity 1, so the graph of f crosses the x-axis at x = - 2. The fourth zero of the function is of
multiplicity 1, so the graph of f crosses the x-axis at x =-3
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