For Exercises 33–36, a. Use transformations of the graphs of y = ( 1 3 ) x (see Exercise 17) and y = ( 1 4 ) x (see Exercise 18) to graph the given function. (See Example 2) b. Write the domain and range in interval notation. c. Write an equation of the asymptote. k ( x ) = − ( 1 3 ) x + 2
For Exercises 33–36, a. Use transformations of the graphs of y = ( 1 3 ) x (see Exercise 17) and y = ( 1 4 ) x (see Exercise 18) to graph the given function. (See Example 2) b. Write the domain and range in interval notation. c. Write an equation of the asymptote. k ( x ) = − ( 1 3 ) x + 2
Solution Summary: The author explains how to graph the function k(x)=- (13 )x+2 using transformation of the graph.
a. Use transformations of the graphs of
y
=
(
1
3
)
x
(see Exercise 17) and
y
=
(
1
4
)
x
(see Exercise 18) to graph the given function. (See Example 2)
b. Write the domain and range in interval notation.
Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045.
2) Find Θ given sec Θ = 4.213.
3) Find Θ given cot Θ = 0.579. Solve the following three right triangles.
B
21.0
34.6° ca
52.5
4)c
26°
5)
A
b
6) B 84.0 a
42°
b
Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N
then dim M = dim N but the converse need not to be true.
B: Let A and B two balanced subsets of a linear space X, show that whether An B and
AUB are balanced sets or nor.
Q2: Answer only two
A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists
ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}.
fe
B:Show that every two norms on finite dimension linear space are equivalent
C: Let f be a linear function from a normed space X in to a normed space Y, show that
continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence
(f(x)) converge to (f(x)) in Y.
Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as
normed space
B: Let A be a finite dimension subspace of a Banach space X, show that A is closed.
C: Show that every finite dimension normed space is Banach space.
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
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