Analyze the polynomial function f(x)=−3(x+4)(x−4)3 using parts (a) through (e). Fill in the ? question marks (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) 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 is a zero of multiplicity ?, so the graph of f touches/crosses <-- (choose one) the x-axis at x=? The greater zero is a zero of multiplicity ?, so the graph of f crosses/touches <--(choose one) 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.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Analyze the polynomial function f(x)=−3(x+4)(x−4)³ using parts (a) through (e). Fill in the ? question marks

(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) 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 is a zero of multiplicity ?, so the graph of f touches/crosses <-- (choose one) the x-axis at

x=?

The greater zero is a zero of multiplicity ?, so the graph of f

crosses/touches <--(choose one) 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.

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