Answers2627 ALGEBRA II AFunction Inverses

Lesson 2.8: Rate of Change Answers

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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
2
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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
3

If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?

A
y = StartFraction 48 Over 6 EndFraction (2)
Option A
B
y = StartFraction 6 Over 48 EndFraction (2)
Option B
C
y = StartFraction (48) (6) Over 2 EndFraction
Option C
D
y = StartFraction 2 Over (48) (6) EndFraction
Option D
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

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
6

If y varies directly as x, and y is 18 when x is 5, which expression can be used to find the value of y when x is 11?

A
y = StartFraction 5 Over 18 EndFraction (11)
Option A
B
y = StartFraction 18 Over 5 EndFraction (11)
Option B
C
y = StartFraction (18) (5) Over 11 EndFraction
Option C
D
y = StartFraction 11 Over (18) (5) EndFraction
Option D
7

What is the average rate of change in f(x) over the interval [4,13]?

Question illustration
A
One-third
Option A
B
Four-thirteenths
Option B
C
Eleven-thirteenths
Option C
D
Eleven-eighths
Option D
8

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
9

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
10

If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?

A
6
B
18
C
30
D
36
11

If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?

A
y = one-ninth
Option A
B
y = two-thirds
Option B
C
54
D
96
12

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
13

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.
14

The cost of soup, s, varies directly with the number of cans, c. When c is 4, the cost is $3. Which graph represents the cost of the soup?

A
On a graph, the x-axis shows the number of cans, from 0 to 10, and the y-axis shows the cost of soup, from 0 to 10. A curve opens up to the right and approaches the x-axis and the y-axis. The vertex is around (1, 1).
Option A
B
On a graph, the x-axis shows the number of cans, from 0 to 10, and the y-axis shows the cost of soup, from 0 to 10. A straight line has a positive slope and goes through (0, 0), (3, 4), and (6, 8).
Option B
C
On a graph, the x-axis shows the number of cans, from 0 to 10, and the y-axis shows the cost of soup, from 0 to 10. A straight line has a positive slope and goes through (0, 0), (4, 3), and (8, 6).
Option C
D
On a graph, the x-axis shows the number of cans, from 0 to 10, and the y-axis shows the cost of soup, from 0 to 10. A curve starts at (0, 0) and opens up to the left. The curve goes through (4, 3) and (5, 6).
Option D

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