Graph the following function using the techniques of shifting, compress of the basic function y=x³ and show all stages. Be sure to identify at least three key points. Find the domain and the range of the function. f(x) = (x+3)³-2 COD Which of the following transformations of y=x³ need to be applied to graph f(x) = (x+3)³-2? Select all that apply. A. Vertical compression B. Reflection about the x-axis C. Horizontal compression D. Reflection about the y-axis E. Vertical stretch F. Horizontal shift G. Horizontal stretch H H. Vertical shift Use the graphing tool to graph the equation. Click to enlarge graph Fill in the missing coordinates of the points that lie on the graph of y=x³ and the corresponding points that lie on the graph of f(x)=(x+3)-2. -10. B B 2 (8- 16 4 12- -24 4 -6 40 Q G

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph
of the basic function y=x³ and show all stages. Be sure to identify at least three key points. Find the domain and the range
of the function.
f(x) = (x+3)³-2
Which of the following transformations of y=x³ need to be applied to graph f(x) = (x+3)³-2? Select all that apply.
A. Vertical compression
B. Reflection about the x-axis
C. Horizontal compression
D. Reflection about the y-axis
E. Vertical stretch
F. Horizontal shift
G.
H. Vertical shift
Horizontal stretch
Use the graphing tool to graph the equation.
Click to
enlarge
graph
Fill in the missing coordinates of the points that lie on the graph of y=x³ and the corresponding points that lie on the graph
of f(x) = (x+3)³-2.
Points that lie on the
graph of y=x³
(Simplify your
answers.)
(-1.)
(0.)
Corresponding points that
lie on the graph of
f(x) = (x+3)³-2
(Type ordered pairs.
Simplify your answer.)
CD
-10
10
10
Q
G
Transcribed Image Text:Graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function y=x³ and show all stages. Be sure to identify at least three key points. Find the domain and the range of the function. f(x) = (x+3)³-2 Which of the following transformations of y=x³ need to be applied to graph f(x) = (x+3)³-2? Select all that apply. A. Vertical compression B. Reflection about the x-axis C. Horizontal compression D. Reflection about the y-axis E. Vertical stretch F. Horizontal shift G. H. Vertical shift Horizontal stretch Use the graphing tool to graph the equation. Click to enlarge graph Fill in the missing coordinates of the points that lie on the graph of y=x³ and the corresponding points that lie on the graph of f(x) = (x+3)³-2. Points that lie on the graph of y=x³ (Simplify your answers.) (-1.) (0.) Corresponding points that lie on the graph of f(x) = (x+3)³-2 (Type ordered pairs. Simplify your answer.) CD -10 10 10 Q G
7
7
Consider the functions f(x)= and g(x)=;
X
x
(a) Find f(g(x)).
(b) Find g(f(x)).
(c) Determine whether the functions f and g are inverses of each other.
(a) What is f(g(x))?
f(g(x)) =
(Simplify your answer.)
Give any values of x that need to be excluded from f(g(x)). Select the correct choice below and fill in any answer boxes within your choice.
O A. x#
(Use a comma to separate answers as needed.)
OB. No values should be excluded from the domain.
(b) What is g(f(x))?
g(f(x)) =
(Simplify your answer.)
Give any values of x that need to be excluded from g(f(x)). Select the correct choice below and fill in any answer boxes within your choice.
O A. x#
(Use a comma to separate answers as needed.)
OB. No values should be excluded from the domain.
(c) Are the functions f and g inverses of each other? Choose the correct answer below.
No
O Yes
Transcribed Image Text:7 7 Consider the functions f(x)= and g(x)=; X x (a) Find f(g(x)). (b) Find g(f(x)). (c) Determine whether the functions f and g are inverses of each other. (a) What is f(g(x))? f(g(x)) = (Simplify your answer.) Give any values of x that need to be excluded from f(g(x)). Select the correct choice below and fill in any answer boxes within your choice. O A. x# (Use a comma to separate answers as needed.) OB. No values should be excluded from the domain. (b) What is g(f(x))? g(f(x)) = (Simplify your answer.) Give any values of x that need to be excluded from g(f(x)). Select the correct choice below and fill in any answer boxes within your choice. O A. x# (Use a comma to separate answers as needed.) OB. No values should be excluded from the domain. (c) Are the functions f and g inverses of each other? Choose the correct answer below. No O Yes
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