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Math Problems
Algebra 2
Average rate of change
What is the average value of
f
(
x
)
=
e
x
2
−
2
x
f(x)=e^{x^{2}-2 x}
f
(
x
)
=
e
x
2
−
2
x
on the interval
[
−
1
,
3
]
[-1,3]
[
−
1
,
3
]
?
\newline
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What is the average value of
h
(
x
)
=
x
3
+
7
x
2
+
3
2
x
2
−
5
x
+
4
h(x)=\frac{x^{3}+7 x^{2}+3}{2 x^{2}-5 x+4}
h
(
x
)
=
2
x
2
−
5
x
+
4
x
3
+
7
x
2
+
3
on the interval
[
−
8
,
−
2
]
[-8,-2]
[
−
8
,
−
2
]
?
\newline
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Given the function
f
(
x
)
=
−
x
2
−
7
x
+
20
f(x)=-x^{2}-7 x+20
f
(
x
)
=
−
x
2
−
7
x
+
20
, determine the average rate of change of the function over the interval
−
8
≤
x
≤
0
-8 \leq x \leq 0
−
8
≤
x
≤
0
.
\newline
Answer:
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Given the function
g
(
x
)
=
x
2
+
8
x
+
12
g(x)=x^{2}+8 x+12
g
(
x
)
=
x
2
+
8
x
+
12
, determine the average rate of change of the function over the interval
−
10
≤
x
≤
−
1
-10 \leq x \leq-1
−
10
≤
x
≤
−
1
.
\newline
Answer:
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Given the function
h
(
x
)
=
x
2
+
8
x
+
10
h(x)=x^{2}+8 x+10
h
(
x
)
=
x
2
+
8
x
+
10
, determine the average rate of change of the function over the interval
−
9
≤
x
≤
−
1
-9 \leq x \leq-1
−
9
≤
x
≤
−
1
.
\newline
Answer:
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Given the function
f
(
x
)
=
x
2
+
10
x
+
19
f(x)=x^{2}+10 x+19
f
(
x
)
=
x
2
+
10
x
+
19
, determine the average rate of change of the function over the interval
−
8
≤
x
≤
−
1
-8 \leq x \leq-1
−
8
≤
x
≤
−
1
.
\newline
Answer:
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Given the function
g
(
x
)
=
x
2
+
x
−
5
g(x)=x^{2}+x-5
g
(
x
)
=
x
2
+
x
−
5
, determine the average rate of change of the function over the interval
−
1
≤
x
≤
3
-1 \leq x \leq 3
−
1
≤
x
≤
3
.
\newline
Answer:
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Given the function
h
(
x
)
=
x
2
+
6
x
+
3
h(x)=x^{2}+6 x+3
h
(
x
)
=
x
2
+
6
x
+
3
, determine the average rate of change of the function over the interval
−
8
≤
x
≤
−
2
-8 \leq x \leq-2
−
8
≤
x
≤
−
2
.
\newline
Answer:
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Given the function
h
(
x
)
=
x
2
−
6
x
+
7
h(x)=x^{2}-6 x+7
h
(
x
)
=
x
2
−
6
x
+
7
, determine the average rate of change of the function over the interval
0
≤
x
≤
4
0 \leq x \leq 4
0
≤
x
≤
4
.
\newline
Answer:
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Given the function
g
(
x
)
=
−
x
2
+
4
x
+
10
g(x)=-x^{2}+4 x+10
g
(
x
)
=
−
x
2
+
4
x
+
10
, determine the average rate of change of the function over the interval
−
1
≤
x
≤
3
-1 \leq x \leq 3
−
1
≤
x
≤
3
.
\newline
Answer:
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Given the function
g
(
x
)
=
x
2
−
8
x
+
14
g(x)=x^{2}-8 x+14
g
(
x
)
=
x
2
−
8
x
+
14
, determine the average rate of change of the function over the interval
−
1
≤
x
≤
10
-1 \leq x \leq 10
−
1
≤
x
≤
10
.
\newline
Answer:
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Given the function
h
(
x
)
=
x
2
−
5
x
+
2
h(x)=x^{2}-5 x+2
h
(
x
)
=
x
2
−
5
x
+
2
, determine the average rate of change of the function over the interval
2
≤
x
≤
9
2 \leq x \leq 9
2
≤
x
≤
9
.
\newline
Answer:
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Given the function
g
(
x
)
=
−
x
2
+
10
x
+
28
g(x)=-x^{2}+10 x+28
g
(
x
)
=
−
x
2
+
10
x
+
28
, determine the average rate of change of the function over the interval
4
≤
x
≤
10
4 \leq x \leq 10
4
≤
x
≤
10
.
\newline
Answer:
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Given the function
g
(
x
)
=
−
x
2
+
6
x
+
12
g(x)=-x^{2}+6 x+12
g
(
x
)
=
−
x
2
+
6
x
+
12
, determine the average rate of change of the function over the interval
−
1
≤
x
≤
6
-1 \leq x \leq 6
−
1
≤
x
≤
6
.
\newline
Answer:
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Given the function
h
(
x
)
=
x
2
−
7
x
+
8
h(x)=x^{2}-7 x+8
h
(
x
)
=
x
2
−
7
x
+
8
, determine the average rate of change of the function over the interval
1
≤
x
≤
8
1 \leq x \leq 8
1
≤
x
≤
8
.
\newline
Answer:
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Given the function
g
(
x
)
=
−
x
2
−
6
x
+
14
g(x)=-x^{2}-6 x+14
g
(
x
)
=
−
x
2
−
6
x
+
14
, determine the average rate of change of the function over the interval
−
5
≤
x
≤
2
-5 \leq x \leq 2
−
5
≤
x
≤
2
.
\newline
Answer:
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Given the function
h
(
x
)
=
−
x
2
−
9
x
+
23
h(x)=-x^{2}-9 x+23
h
(
x
)
=
−
x
2
−
9
x
+
23
, determine the average rate of change of the function over the interval
−
7
≤
x
≤
1
-7 \leq x \leq 1
−
7
≤
x
≤
1
.
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
2
−
x
+
7
f(x)=-x^{2}-x+7
f
(
x
)
=
−
x
2
−
x
+
7
, determine the average rate of change of the function over the interval
−
4
≤
x
≤
2
-4 \leq x \leq 2
−
4
≤
x
≤
2
.
\newline
Answer:
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Given the function
g
(
x
)
=
−
x
2
−
7
x
+
15
g(x)=-x^{2}-7 x+15
g
(
x
)
=
−
x
2
−
7
x
+
15
, determine the average rate of change of the function over the interval
−
5
≤
x
≤
−
1
-5 \leq x \leq-1
−
5
≤
x
≤
−
1
.
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
2
+
3
x
+
6
f(x)=-x^{2}+3 x+6
f
(
x
)
=
−
x
2
+
3
x
+
6
, determine the average rate of change of the function over the interval
−
1
≤
x
≤
5
-1 \leq x \leq 5
−
1
≤
x
≤
5
.
\newline
Answer:
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Given the function
g
(
x
)
=
−
x
2
−
8
x
+
24
g(x)=-x^{2}-8 x+24
g
(
x
)
=
−
x
2
−
8
x
+
24
, determine the average rate of change of the function over the interval
−
6
≤
x
≤
1
-6 \leq x \leq 1
−
6
≤
x
≤
1
.
\newline
Answer:
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Given the function
h
(
x
)
=
x
2
−
6
x
+
1
h(x)=x^{2}-6 x+1
h
(
x
)
=
x
2
−
6
x
+
1
, determine the average rate of change of the function over the interval
−
1
≤
x
≤
4
-1 \leq x \leq 4
−
1
≤
x
≤
4
.
\newline
Answer:
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Given the function
f
(
x
)
=
x
2
−
10
x
+
18
f(x)=x^{2}-10 x+18
f
(
x
)
=
x
2
−
10
x
+
18
, determine the average rate of change of the function over the interval
−
1
≤
x
≤
6
-1 \leq x \leq 6
−
1
≤
x
≤
6
.
\newline
Answer:
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Given the function
g
(
x
)
=
x
2
−
9
x
+
12
g(x)=x^{2}-9 x+12
g
(
x
)
=
x
2
−
9
x
+
12
, determine the average rate of change of the function over the interval
1
≤
x
≤
7
1 \leq x \leq 7
1
≤
x
≤
7
.
\newline
Answer:
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Given the function
f
(
x
)
=
x
2
+
9
x
+
12
f(x)=x^{2}+9 x+12
f
(
x
)
=
x
2
+
9
x
+
12
, determine the average rate of change of the function over the interval
−
5
≤
x
≤
−
1
-5 \leq x \leq-1
−
5
≤
x
≤
−
1
.
\newline
Answer:
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Given the function
h
(
x
)
=
−
x
2
+
7
x
+
20
h(x)=-x^{2}+7 x+20
h
(
x
)
=
−
x
2
+
7
x
+
20
, determine the average rate of change of the function over the interval
−
2
≤
x
≤
9
-2 \leq x \leq 9
−
2
≤
x
≤
9
.
\newline
Answer:
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What is the average value of
3
x
2
+
4
x
3 x^{2}+4 x
3
x
2
+
4
x
on the interval
2
≤
x
≤
6
2 \leq x \leq 6
2
≤
x
≤
6
?
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Andrei has a glass tank that he would like to fill with marbles and water.
\newline
W
(
m
)
W(m)
W
(
m
)
models the amount of water Andrei needs (in liters) if he uses
m
m
m
marbles.
\newline
m
m
m
10
10
10
32
32
32
68
68
68
\newline
W
(
m
)
W(m)
W
(
m
)
36
36
36
.
5
5
5
28
28
28
.
8
8
8
16
16
16
.
2
2
2
\newline
\end{tabular}
\newline
When does the necessary amount of water decrease faster?
\newline
Choose
1
1
1
answer:
\newline
(A) Between
10
10
10
marbles and
32
32
32
marbles
\newline
(B) Between
32
32
32
marbles and
68
68
68
marbles
\newline
(C) The necessary amount of water decreases at the same rate over both intervals
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