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Math Problems
Algebra 1
Linear functions over unit intervals
How does
g
(
x
)
=
1
0
x
g(x) = 10^x
g
(
x
)
=
1
0
x
change over the interval from
x
=
3
x = 3
x
=
3
to
x
=
4
x = 4
x
=
4
?
\newline
Choices:
\newline
g
(
x
)
g(x)
g
(
x
)
increases by a factor of
10
10
10
\newline
g
(
x
)
g(x)
g
(
x
)
increases by a factor of
100
100
100
\newline
g
(
x
)
g(x)
g
(
x
)
decreases by
20
%
20\%
20%
\newline
g
(
x
)
g(x)
g
(
x
)
decreases by a factor of
10
10
10
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How does
f
(
t
)
=
8
t
f(t)=8^t
f
(
t
)
=
8
t
change over the interval from
t
=
4
t=4
t
=
4
to
t
=
6
t=6
t
=
6
?
\newline
Choices:
\newline
f(t) decreases by a factor of 16
\text{f(t) decreases by a factor of 16}
f(t) decreases by a factor of 16
\newline
f(t) increases by 16%
\text{f(t) increases by 16\%}
f(t) increases by 16%
\newline
f(t) decreases by factor of 8
\text{f(t) decreases by factor of 8}
f(t) decreases by factor of 8
\newline
f(t) increases by a factor of 64
\text{f(t) increases by a factor of 64}
f(t) increases by a factor of 64
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How does
f
(
x
)
=
5
x
f(x)=5^x
f
(
x
)
=
5
x
change over the interval from
x
=
1
x=1
x
=
1
to
x
=
3
x=3
x
=
3
?
\newline
Choices:
\newline
f(x) decreases by a factor of 10
\text{f(x) decreases by a factor of 10}
f(x) decreases by a factor of 10
\newline
f(x) increases by 10%
\text{f(x) increases by 10\%}
f(x) increases by 10%
\newline
f(x) increases by a factor of 25
\text{f(x) increases by a factor of 25}
f(x) increases by a factor of 25
\newline
f(x) increases by a factor of 10
\text{f(x) increases by a factor of 10}
f(x) increases by a factor of 10
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How does
f
(
t
)
=
7
t
f(t)=7^t
f
(
t
)
=
7
t
change over the interval from
t
=
1
t=1
t
=
1
to
t
=
3
t=3
t
=
3
?
\newline
Choices:
\newline
f(t) decreases by a factor of 7
\text{f(t) decreases by a factor of 7}
f(t) decreases by a factor of 7
\newline
f(t) increases by factor of 7
\text{f(t) increases by factor of 7}
f(t) increases by factor of 7
\newline
f(t) decreases by 7%
\text{f(t) decreases by 7\%}
f(t) decreases by 7%
\newline
f(t) increases by a factor of 49
\text{f(t) increases by a factor of 49}
f(t) increases by a factor of 49
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How does
h
(
t
)
=
9
t
h(t) = 9^t
h
(
t
)
=
9
t
change over the interval from
t
=
1
t=1
t
=
1
to
t
=
3
t=3
t
=
3
?
\newline
Choices:
\newline
h(t) increases by 9%
\text{h(t) increases by 9\%}
h(t) increases by 9%
\newline
h(t) increases by a factor of 81
\text{h(t) increases by a factor of 81 }
h(t) increases by a factor of 81
\newline
h(t) decreases by a factor of 9%
\text{h(t) decreases by a factor of 9\%}
h(t) decreases by a factor of 9%
\newline
h(t) decreases by a factor of 18
\text{h(t) decreases by a factor of 18}
h(t) decreases by a factor of 18
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How does
g
(
x
)
=
6
x
g(x) = 6^x
g
(
x
)
=
6
x
change over the interval from
x
=
2
x = 2
x
=
2
to
x
=
3
x = 3
x
=
3
?
\newline
Choices:
\newline
(A)
g
(
x
)
g(x)
g
(
x
)
increases by a factor of
6
6
6
\newline
(B)
g
(
x
)
g(x)
g
(
x
)
increases by
600
%
600\%
600%
\newline
(C)
g
(
x
)
g(x)
g
(
x
)
decreases by
6
%
6\%
6%
\newline
(D)
g
(
x
)
g(x)
g
(
x
)
increases by
6
%
6\%
6%
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How does
g
(
x
)
=
9
x
g(x) = 9^x
g
(
x
)
=
9
x
change over the interval from
x
=
5
x = 5
x
=
5
to
x
=
6
x = 6
x
=
6
?
\newline
Choices:
\newline
(A)
g
(
x
)
g(x)
g
(
x
)
increases by
900
%
900\%
900%
\newline
(B)
g
(
x
)
g(x)
g
(
x
)
decreases by
9
9
9
\newline
(C)
g
(
x
)
g(x)
g
(
x
)
decreases by
9
%
9\%
9%
\newline
(D)
g
(
x
)
g(x)
g
(
x
)
increases by a factor of
9
9
9
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How does
f
(
t
)
=
−
2
t
−
7
f(t)=-2t-7
f
(
t
)
=
−
2
t
−
7
change over the interval from
t
=
−
7
t=-7
t
=
−
7
to
t
=
−
6
t=-6
t
=
−
6
?
\newline
Choices:
\newline
[
f(t) decreases by
2
]
\left[\text{f(t) decreases by } 2\right]
[
f(t) decreases by
2
]
\newline
[
f(t) increases by
2
]
\left[\text{f(t) increases by } 2\right]
[
f(t) increases by
2
]
\newline
[
f(t) increases by
200
%
]
\left[\text{f(t) increases by } 200\%\right]
[
f(t) increases by
200%
]
\newline
[
f(t) decreases by a factor of
2
]
\left[\text{f(t) decreases by a factor of } 2\right]
[
f(t) decreases by a factor of
2
]
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