Analyze the polynomial function f(x) = x³ + x²-20x using parts (a) through (h) below. (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 (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) (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 (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The least zero is of multiplicity, so the graph of f The middle zero is of multiplicity, so the graph of f The greatest zero is of multiplicity, so the graph of f the x-axis at x = the x-axis at x = the x-axis at x =

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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It is only one question. However, you need to answer from (a) to (h). Make sure to answer all to each item. Also, highlight clearly the answer to each type as soon as possible!

(f) Use the information in parts (a) through (e) to draw a complete graph of the function by hand. Choose the correct graph below.
O A.
O B.
Q
G
(g) From the graph, find the range of the polynomial function.
The range of the polynomial function fis
(Type your answer in interval notation. Round to the nearest hundredth as needed.)
(h) Use the graph to determine where the function is increasing and where it is decreasing.
The function is increasing on the interval(s).
(Type your answer in interval notation. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
The function is decreasing on the interval(s).
(Type your answer in interval notation. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
O C.
✔
O D.
E
e
17
Transcribed Image Text:(f) Use the information in parts (a) through (e) to draw a complete graph of the function by hand. Choose the correct graph below. O A. O B. Q G (g) From the graph, find the range of the polynomial function. The range of the polynomial function fis (Type your answer in interval notation. Round to the nearest hundredth as needed.) (h) Use the graph to determine where the function is increasing and where it is decreasing. The function is increasing on the interval(s). (Type your answer in interval notation. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.) The function is decreasing on the interval(s). (Type your answer in interval notation. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.) O C. ✔ O D. E e 17
Analyze the polynomial function f(x) = x³ + x² - 20x using parts (a) through (h) below.
(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
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)
The y-intercept(s) is/are
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)
(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
(Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.)
The least zero is of multiplicity, so the graph of f
The middle zero is of multiplicity so the graph of f
The greatest zero is of multiplicity, so the graph of f
(d) Use a graphing utility to graph the function. Use the viewing window Xmin=-10, Xmax = 10, Xscl = 1, Ymin - 60, Ymax = 60, Y scl = 6. Choose the correct graph below.
O A.
Q
Q
the x-axis at x =
the x-axis at x =
the x-axis at x =
O B.
C
Q
(e) Approximate the turning points of the graph.
The turning point(s) of the graph is/are
(Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Use a comma to separate answers as needed.)
O C.
HA
O D.
A
Q
Transcribed Image Text:Analyze the polynomial function f(x) = x³ + x² - 20x using parts (a) through (h) below. (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 (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) (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 (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The least zero is of multiplicity, so the graph of f The middle zero is of multiplicity so the graph of f The greatest zero is of multiplicity, so the graph of f (d) Use a graphing utility to graph the function. Use the viewing window Xmin=-10, Xmax = 10, Xscl = 1, Ymin - 60, Ymax = 60, Y scl = 6. Choose the correct graph below. O A. Q Q the x-axis at x = the x-axis at x = the x-axis at x = O B. C Q (e) Approximate the turning points of the graph. The turning point(s) of the graph is/are (Type an ordered pair. Round each coordinate to the nearest hundredth as needed. Use a comma to separate answers as needed.) O C. HA O D. A Q
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