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Math Problems
Algebra 2
Identify linear and exponential functions
A function
h
(
t
)
h(t)
h
(
t
)
increases by a factor of
6
6
6
over every unit interval in
t
t
t
and
h
(
0
)
=
1
h(0) = 1
h
(
0
)
=
1
.
\newline
Which could be a function rule for
h
(
t
)
h(t)
h
(
t
)
?
\newline
Choices:
\newline
(A)
h
(
t
)
=
6
t
h(t) = 6^t
h
(
t
)
=
6
t
\newline
(B)
h
(
t
)
=
0.9
4
t
h(t) = 0.94^t
h
(
t
)
=
0.9
4
t
\newline
(C)
h
(
t
)
=
1
6
t
h(t) = \frac{1}{6^t}
h
(
t
)
=
6
t
1
\newline
(D)
h
(
t
)
=
6
t
h(t) = 6t
h
(
t
)
=
6
t
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Which equation has a constant of proportionality equal to
5
5
5
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
5
x
y=5 x
y
=
5
x
\newline
B
y
=
10
5
x
y=\frac{10}{5} x
y
=
5
10
x
\newline
C)
y
=
5
25
x
y=\frac{5}{25} x
y
=
25
5
x
\newline
(D)
y
=
1
2
x
y=\frac{1}{2} x
y
=
2
1
x
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Which equation has a constant of proportionality equal to
1
1
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
10
11
x
y=\frac{10}{11} x
y
=
11
10
x
\newline
(B)
y
=
7
8
x
y=\frac{7}{8} x
y
=
8
7
x
\newline
(C)
y
=
3
15
x
y=\frac{3}{15} x
y
=
15
3
x
\newline
(D)
y
=
x
y=x
y
=
x
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Which value for the constant
c
c
c
makes
z
=
−
5
4
z=-\frac{5}{4}
z
=
−
4
5
an extraneous solution in the following equation?
\newline
4
z
+
9
=
c
z
+
8
c
=
□
\begin{array}{l} \sqrt{4 z+9}=c z+8 \\ c=\square \end{array}
4
z
+
9
=
cz
+
8
c
=
□
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What is the amplitude of
\newline
h
(
x
)
=
7
sin
(
3
π
4
x
−
π
4
)
+
6
?
h(x)=7 \sin \left(\frac{3 \pi}{4} x-\frac{\pi}{4}\right)+6 ?
h
(
x
)
=
7
sin
(
4
3
π
x
−
4
π
)
+
6
?
\newline
units
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What is the amplitude of
\newline
g
(
x
)
=
cos
(
2
π
3
x
)
+
1
?
g(x)=\cos \left(\frac{2 \pi}{3} x\right)+1 ?
g
(
x
)
=
cos
(
3
2
π
x
)
+
1
?
\newline
units
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What is the period of
\newline
y
=
7
sin
(
−
3
π
4
x
−
π
4
)
+
6
?
y=7 \sin \left(-\frac{3 \pi}{4} x-\frac{\pi}{4}\right)+6 ?
y
=
7
sin
(
−
4
3
π
x
−
4
π
)
+
6
?
\newline
Give an exact value.
\newline
units
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Every year
39
39
39
million cars cross the Golden Gate Bridge in San Francisco.
\newline
Which kind of function best models the relationship between time and the cumulative number of cars that have crossed the Golden Gate Bridge?
\newline
Choose
1
1
1
answer:
\newline
(A) Linear
\newline
(B) Exponential
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Fidel has a rare coin worth
$
550
\$ 550
$550
. Each decade, the coin's value increases by
10
%
10 \%
10%
.
\newline
Which kind of function best models the relationship between time and the coin's value?
\newline
Choose
1
1
1
answer:
\newline
(A) Linear
\newline
(B) Exponential
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The number of visitors to the Eiffel Tower in Paris increases by
1.5
%
1.5\%
1.5%
each year.
\newline
Which kind of function best models the relationship between time and the number of visitors to the Eiffel Tower?
\newline
Choose
1
1
1
answer:
\newline
(A) Linear
\newline
(B) Exponential
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Enrico deposited
$
2000
\$ 2000
$2000
in a savings account. Each month he will deposit an additional
$
25
\$ 25
$25
.
\newline
Which kind of function best models the relationship between time and the total amount in the savings account?
\newline
Choose
1
1
1
answer:
\newline
(A) Linear
\newline
(B) Exponential
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A function
f
(
x
)
f(x)
f
(
x
)
increases by
6
6
6
over every unit interval in
x
x
x
and
f
(
0
)
=
0
f(0) = 0
f
(
0
)
=
0
.
\newline
Which could be a function rule for
f
(
x
)
f(x)
f
(
x
)
?
\newline
Choices:
\newline
(A)
f
(
x
)
=
6
x
f(x) = 6x
f
(
x
)
=
6
x
\newline
(B)
f
(
x
)
=
6
x
f(x) = 6^x
f
(
x
)
=
6
x
\newline
(C)
f
(
x
)
=
1
6
x
f(x) = \frac{1}{6^x}
f
(
x
)
=
6
x
1
\newline
(D)
f
(
x
)
=
x
6
f(x) = \frac{x}{6}
f
(
x
)
=
6
x
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