The graphs labeled (a)-(d) in the figure represent y = 3 r , y = 5 x , y = ( 1 3 ) x , and y = ( 1 5 ) 2 . but not necessarily in that order. Which is which? Describe the process that enables you to make this decision.
The graphs labeled (a)-(d) in the figure represent y = 3 r , y = 5 x , y = ( 1 3 ) x , and y = ( 1 5 ) 2 . but not necessarily in that order. Which is which? Describe the process that enables you to make this decision.
Solution Summary: The author explains that each function is an exponential function of the form rx.
The graphs labeled (a)-(d) in the figure represent
y
=
3
r
,
y
=
5
x
,
y
=
(
1
3
)
x
,
and
y
=
(
1
5
)
2
. but not necessarily in that order. Which is which? Describe the process that enables you to make this decision.
(1) Let M and N be non-empty subsets of a linear space X, show that whether
= U or not, and show that there whether exsits a liear function
from P₂(x) into R' which onto but not one-to-one or not.
ام
(2) Let R be a field of real numbers and P,(x)=(a+bx+cx? / a,b,ce R} be a vector space
over R, show that whether there exsit two hyperspaces A and B such that AUB is a
hyperspace or not.
(3) Let A be an affine set in a linear space X over afield F and tEA, show that A-t is a
subspace of Xand show that if M and N are balanced sets then M+N is balanced set.
(4) Write the definition of bounded set in a normed space, and write with prove
an equivalent statement to definition.
(5) Let d be a metric on a linear space X over a field F, write conditions on d in order to
get that there is a norm on X induced dy d and prove that.
(6) Let M be a non-empty subset of a normed space X, show that xEcl(M) iff for any r>o
there exsits yEM such that llx-yll
Find all solutions to the following equation. Do you get any extraneous solutions? Explain why or why
not.
2
2
+
x+1x-1
x21
Show all steps in your process. Be sure to state your claim, provide your evidence, and provide your
reasoning before submitting.
Directions: For problems 1 through 3, read each question carefully and be sure to show all work.
1. What is the phase shift for y = 2sin(2x-)?
2. What is the amplitude of y = 7cos(2x+л)?
3. What is the period of y = sin(3x-π)?
Directions: For problems 4 and 5, you were to compare and contrast the two functions in each problem situation. Be sure to
include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-maximums, and any phase shift
between the two graphs. Write in complete sentences.
4. y 3sin(2x) and y = 3cos(2x)
5. y 4sin(2x) and y = cos(3x- -플)
Chapter 4 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Algebra and Trigonometry (6th Edition)
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