Section 1.3 Version 1
1. The following table shows the income tax T owed in a certain state as a function of the
taxable income I, both measured in dollars. Make a table showing, for each of the
intervals in the tax table below, the average rate of change in T.
I = Taxable income
12,100
14,400
15,500
17,600
T = Tax owed
450
561
741
981
A)
Income interval
From 12,100 to 14,400
From 14,400 to 15,500
From 15,500 to 17,600
Average rate of change in T
0.05
0.16
0.11
B)
Income interval
From 12,100 to 14,400
From 14,400 to 15,500
From 15,500 to 17,600
Average rate of change in T
0.25
0.56
0.71
C)
Income interval
Average rate of change in T
From 12,100 to 14,400
From 14,400 to 15,500
From 15,500 to 17,600
0.56
0.71
0.25
D)
Income interval
From 12,100 to 14,400
From 14,400 to 15,500
From 15,500 to 17,600
Average rate of change in T
0.71
0.25
0.56
E)
Income interval
From 12,100 to 14,400
From 14,400 to 15,500
From 15,500 to 17,600
Average rate of change in T
0.71
0.56
0.25
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2. The following table shows the income tax T owed in a certain state as a function of the
taxable income I, both measured in dollars. Would you expect T to have a limiting
value? Why?
I = Taxable income
T = Tax owed
12,300
484
14,200
550
15,800
750
17,900
992
A) Yes, because the general trend in the average rate of change is not continuously
decreasing.
B) No, because the average rate of change for 12,300 to 15,800 is not decreasing.
C) Yes, because the average rate of change for 14,200 to 15,800 is decreasing.
D) No, because the average rate of change does not approach 0 as I decreases.
E) Yes, because the average rate of change for 12,300 to 17,900 is decreasing.
3. The Margaria-Kalamen test is used by physical educators as a measure of leg strength.
An individual runs up a staircase, and the elapsed time from the third to the ninth step is
recorded. The power score is calculated using a formula involving the individual’s
weight, the height of the stairs, and the running time. The following table shows the
power scores required of men for an excellent rating for selected ages. During which 10year period from age 25 to 55 would you expect to see the greatest decrease in leg
power?
Age
18
25
35
45
55
A)
B)
C)
D)
E)
Power score for
excellent rating
220
212
175
121
95
18 to 25
25 to 35
35 to 45
45 to 55
25 to 55
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4. The following is the graph of a function f = f ( x ) . What is the value of f (1.2 ) . Round
your answer to one decimal place.
A)
B)
C)
D)
E)
2.1
1.7
2.5
2.7
1.9
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5. The following is the graph of a function f = f ( x ) . What is the smallest value of x for
which f ( x ) = 2 . Round your answer to one decimal place.
A)
B)
C)
D)
E)
3.6
1.6
0.8
1.2
4.0
6. The following is the graph of the function f(x). Where is the graph increasing?
A)
B)
C)
D)
E)
from –10 to 0
from –1 to 10
from –5 to 1
from –2 to 10
from –5 to 5
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7. Sketch the graph of a function f = f (x) if f has a maximum value of 1.33 when x = –
0.33, and f has a zero at x = –1.
A)
B)
C)
D)
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E)
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8. Sketch a graph that is always decreasing but starts out concave up and then changes to
concave down. Mark the point of inflection in your graph.
A)
B)
C)
D)
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E)
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9. A stock market investment of $12,000 was made in 1970. During the decade of the
1970s, the stock lost half its value. Beginning in 1980, the value increased until it
reached $28,000 in 1990. After that its value has remained stable. Let v = v(d) denote
the value of the stock, in dollars, as a function of the date d. Make a graph of v against d.
A)
B)
C)
D)
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E)
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10. The graph below shows the mean flow F for the Arkansas River, in cubic feet of water
per second, as a function of the time t, in months, since the start of the year. The flow is
measured near the river's headwaters in the Rocky Mountains.
Estimate the average rate of change per month in the flow during the first 5 months of
the year
A) 90
B) 110
C) 480
D) 240
E) 170
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11. The graph below shows the temperature T = T(v) adjusted for wind chill as a function of
the velocity v of the wind when the thermometer reads 30 degrees Fahrenheit. The
adjusted temperature T shows the temperature that has an equivalent cooling power
when there is no wind.
At what wind speed is the temperature adjusted for wind chill equal to –5?
A) 20 mph
B) 11 mph
C) 40 mph
D) 13 mph
E) 5 mph
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12. The graph below shows the temperature T = T(v) adjusted for wind chill as a function of
the velocity v of the wind when the thermometer reads 30 degrees Fahrenheit. The
adjusted temperature T shows the temperature that has an equivalent cooling power
when there is no wind.
If v changes from 10 mph to 15 mph, what would be the change in the corresponding
T(v) values?
A) from 8 degrees Fahrenheit to 16 degrees Fahrenheit
B) from –3 degrees Fahrenheit to 4 degrees Fahrenheit
C) from 7 degrees Fahrenheit to 27 degrees Fahrenheit
D) from 2.2 degrees Fahrenheit to 3.8 degrees Fahrenheit
E) from 15 degrees Fahrenheit to 8 degrees Fahrenheit
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13. The graph below shows the number T = T(d) of tornadoes reported by the Oklahoma
Climatological Survey.
Estimate the average yearly decrease in tornadic activity from 2001 to 2002?
A) 88 tornadoes per year
B) 66 tornadoes per year
C) 42 tornadoes per year
D) 57 tornadoes per year
E) 76 tornadoes per year
14. The graph below shows the number T = T(d) of tornadoes reported by the Oklahoma
Climatological Survey. Estimate the the average yearly rate of change in tornadic
activity from 1999 to 2003?
A)
B)
C)
D)
E)
16.00 tornadoes per year
16.80 tornadoes per year
–16.00 tornadoes per year
18.80 tornadoes per year
24.00 tornadoes per year
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15. Suppose the amount of carbon dioxide in the air is influenced by several factors,
including respiration of plants. The following figure shows the concentration of carbon
dioxide in parts per million (PPM) in a closed (that is, unventilated) greenhouse on a
cold, clear day during a 24-hour period beginning at 6 a.m. When is carbon dioxide in
the greenhouse at its highest concentration?
A) The maximum concentration is attained over the entire interval from about 9 a.m.
to about 2 p.m.
B) The maximum concentration is attained over the entire interval from about 6 a.m.
to about 9 a.m.
C) The maximum concentration is attained at about 2 p.m.
D) The maximum concentration is attained at about 10 a.m.
E) The maximum concentration is attained at about 2 a.m.
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16. Fertilizer can increase crop production, but the cost of the fertilizer must be taken into
account. The following curved graph shows the added bushels per acre of corn that
resulted from fertilizer application versus pounds per acre of nitrogen applied. The
straight line shows the cost (in bushels of corn, not dollars) versus pounds per acre of
nitrogen applied. How many pounds per acre of nitrogen should be applied to achieve
maximum profit?
A) about 120 pounds of nitrogen per acre should be applied to produce maximum
profit
B) nitrogen should not be applied to produce maximum profit
C) about 70 pounds of nitrogen per acre should be applied to produce maximum profit
D) about 40 pounds of nitrogen per acre should be applied to produce maximum profit
E) about 100 pounds of nitrogen per acre should be applied to produce maximum
profit
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Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
A
D
C
A
D
A
C
B
E
D
C
E
C
C
B
C
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