In Exercises 19-24, the graph of an exponential function is given Select the function for each graph from the following options: f ( x ) = 3 r , g ( x ) = 3 r − 1 , h ( x ) = 3 r − 1 , F ( x ) = − 3 r , G ( x ) = 3 − r , I I ( x ) = − 3 − x .
In Exercises 19-24, the graph of an exponential function is given Select the function for each graph from the following options: f ( x ) = 3 r , g ( x ) = 3 r − 1 , h ( x ) = 3 r − 1 , F ( x ) = − 3 r , G ( x ) = 3 − r , I I ( x ) = − 3 − x .
Solution Summary: The author explains the function g(x)=3x-1, which corresponds to the given graph.
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Q.1) Classify the following statements as a true or false statements:
a. If M is a module, then every proper submodule of M is contained in a maximal
submodule of M.
b. The sum of a finite family of small submodules of a module M is small in M.
c. Zz is directly indecomposable.
d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M.
e. The Z-module has two composition series.
Z
6Z
f. Zz does not have a composition series.
g. Any finitely generated module is a free module.
h. If O→A MW→ 0 is short exact sequence then f is epimorphism.
i. If f is a homomorphism then f-1 is also a homomorphism.
Maximal C≤A if and only if is simple.
Sup
Q.4) Give an example and explain your claim in each case:
Monomorphism not split.
b) A finite free module.
c) Semisimple module.
d) A small submodule A of a module N and a homomorphism op: MN, but
(A) is not small in M.
I need diagram with solutions
T. Determine the least common
denominator and the domain for the
2x-3
10
problem:
+
x²+6x+8
x²+x-12
3
2x
2. Add:
+
Simplify and
5x+10 x²-2x-8
state the domain.
7
3. Add/Subtract:
x+2 1
+
x+6
2x+2 4
Simplify and state the domain.
x+1
4
4. Subtract:
-
Simplify
3x-3
x²-3x+2
and state the domain.
1
15
3x-5
5. Add/Subtract:
+
2
2x-14
x²-7x
Simplify and state the domain.
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