AnswersINMT3 Integrated Math 3 Sem 1 26-27Rate of Change

Rate of Change Answers

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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
2
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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
3

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
4

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
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

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
7

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
8

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
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 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

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