Rate of Change Answers

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The average rate of change of g(x) between x = 4 and x = 7 is . Which statement must be true?

Question illustration
A
g (7) minus g (4) = five-sixths
Option A
B
StartFraction g (7 minus 4) Over 7 minus 4 EndFraction = five-sixths
Option B
C
StartFraction g (7) minus g (4) Over 7 minus 4 EndFraction = five-sixths
Option C
D
StartFraction g (7) Over g (4) EndFraction = five-sixths
Option D
2
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The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall?

Question illustration
A
h(3) – h(0)
B
h (three-thirds) minus h (zero-thirds)
Option B
C
StartFraction h (3) Over 3 EndFraction
Option C
D
StartFraction h (3) minus h (0) Over 3 EndFraction
Option D
3

If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this relation?

A
10
B
40
C
100
D
198
4

T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released. The average rate of change in T(d) for the interval d = 4 and d = 10 is 0. Which statement must be true?

A
The same number of tickets was sold on the fourth day and tenth day.
B
No tickets were sold on the fourth day and tenth day.
C
Fewer tickets were sold on the fourth day than on the tenth day.
D
More tickets were sold on the fourth day than on the tenth day.
5

The graph shows the distance a ball has traveled x seconds after it was thrown. What is the average speed between 2 seconds and 8 seconds.

Question illustration
A
0.5 meters per second
B
0.8 meters per second
C
2 meters per second
D
3 meters per second
6

If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?

A
One-fifth
Option A
B
Four-fifths
Option B
C
5
D
16
7

Calculate the average rate of change of a function over a specified interval. Which expression can be used to determine the average rate of change in f(x) over the interval ?

Question illustration
A
f(9 – 2)
B
f(9) – f(2)
C
StartFraction f (9 minus 2) Over 9 minus 2 EndFraction
Option C
D
StartFraction f (9) minus f (2) Over 9 minus 2 EndFraction
Option D
8

If y varies directly as x, and y is 12 when x is 1.2, what is the constant of variation for this relation?

A
1
B
10
C
10.8
D
14.4
9

Maria created a graph of B(t), the temperature over time. For the interval between t = 3 and t = 7, the average rate of change in her graph of B(t) is 8. Which statement must be true?

A
The temperature was 8 degrees higher when t = 7 than when t = 3.
B
The temperature was 8 times higher when t = 7 than when t = 3.
C
The temperature was 32 degrees higher when t = 7 than when t = 3.
D
The temperature was 2 degrees higher when t = 7 than when t = 3.
10

Which relation is a direct variation that contains the ordered pair (2, 7)?

A
y = 4x – 1
B
y = StartFraction 7 Over x EndFraction
Option B
C
y = two-sevenths x
Option C
D
y = seven-halves x
Option D

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