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Q:
Are these points collinear? (Answer "Yes" or "No".)
(7, -8), (9, -10), and (11, -11)
Q:
The following graph shows the average ACT score for students graduating from Mascoot High School by year. Find the slope of the line from 1990 to 1995.
Q:
Find the value of x such that the line that passes through the points (-6,2) and (x,2) has a slope of .
Q:
Find the value of y such that the line that passes through the points (0, y ) and (16,14) has a slope of .
Q:
Find the slope of the line that passes through the points (7,-8) and (27,4).
Q:
Find the slope of the line that passes through the points (-1,-0.8) and (3,26.4).
Q:
Find the slope of the line through the points (-9.2,6.3) and (1.6,27.9).
Q:
Find the value of y so that the line through the points (9.6,y) and (-5.7,-12.2) has slope 1
Q:
Find the value of y so that the line through the points (-9.3,-8.9) and (-2.1,y) has slope -2
Q:
Find the value of x so that the line through the points (x,-9) and (6.8,7.6) has slope 1
Q:
Find the value of x so that the line through the points (2.9,-0.8) and (x,-44.3) has slope 5
Q:
Find the value of m that satisfies the equation.
Q:
Find the value of y that satisfies the equation.
Q:
Find the value of y that satisfies the equation.
Q:
Find the value of x that satisfies the equation.
Q:
Find the value of x that satisfies the equation.
Q:
Use the graph below to complete the sentence. The average rate of change from point B to point E is:
A) negative.
B) zero.
C) positive.
Q:
Use the graph below to complete the sentence. The average rate of change from point B to point C is:
A) negative.
B) zero.
C) positive.
Q:
Which graph has a negative slope
A) B) C)
Q:
Which choice best describes the slope of the graph pictured? A) negative
B) positive
C) zero
Q:
The average costs, by year, of a 3 bedroom, 2 bath, single-family house in Chetek, WI, are listed in this table. Year
Average Cost
Average Rate of Change 1975
$48,702.21
NA 1980 $969.04 1985 1990
$63,939.52
$1,420.53 1995
$69,908.18 2000 2005
$91,051.19
$1,978.24 Fill in the missing number in the table for each time period. (Round each answer to 2 decimal places.)
Q:
The average costs, by year, of a 3 bedroom, 2 bath, single-family house in Chetek, WI, are listed in this table. Year
Average Cost
Average Rate of Change 1975
$49,578.07
NA 1980
$53,206.18 1985
$56,896.04 1990
$63,986.77 1995
$68,890.75 2000
$80,911.14 2005
$90,306.19 Fill in the average rate of change for each time period. (Round each answer to 2 decimal places.)
Q:
The following table gives information about the population of Barron County by decade. Year
Population (1,000s) 1960
38.7 1970
40.8 1980
42.3 1990
43.4 2000
46.3 2010
49.5 Assuming the annual rate of change was equal to the average rate of change, what would you predict the population (in 1,000s) to be in 2008? (Round the answer to the nearest 0.1 thousand.)
Q:
The following table gives information about the population of Barron County by decade. Year
Population (1,000s) 1960
39.2 1970
41.3 1980
42.8 1990
43.9 2000
46.8 2010
50 Construct a graph of the average rate of change by decade.
Q:
The following table shows the size of the graduating senior class at BLE high school for several years. Year
Number of Students in Graduating Class 1985
131 1990
145 1995
148 2000
149 2005
147 2010
135 Find the total change in the size of the graduating class between 1985 and 1990.
Q:
The following table shows the size of the graduating senior class at BLE high school for several years. Year
Number of Students in Graduating Class 1985
139 1990
155 1995
166 2000
164 2005
161 2010
149 Is the average rate of change increasing, decreasing, or constant throughout?
Q:
The following table shows the size of the graduating senior class at BLE high school for several years. Year
Number of Students in Graduating Class 1985
132 1990
148 1995
158 2000
154 2005
147 2010
135 Which 5 year period has the largest positive rate of change in the size of the graduating class?
Q:
The following table shows the size of the graduating senior class at BLE high school for several years. Year
Number of Students in Graduating Class 1985
123 1990
125 1995
135 2000
140 2005
134 2010
111 Find the average rate of change in the size of the graduating class between 1990 and 1995. (Round the answer to 2 decimal places if necessary.)
Q:
Choose the graph that is described by the following sentence:
As x increases, the function decreases at constant rate.
A) B) C) D)
Q:
Complete the sentence to describe the graph shown: A) As x increases, the function decreases at increasing rate.
B) As x increases, the function decreases at decreasing rate.
C) As x increases, the function increases at increasing rate.
D) As x increases, the function increases at decreasing rate.
Q:
Complete the sentence to describe the graph shown: As x increases, the function A)____________(increases/decreases) at B)_____________ (an increasing/a decreasing/a constant) rate.
Q:
If the function is decreasing, then the average rate of change is ___________.
A) positive
B) zero
C) negative
Q:
If the function is increasing, then the average rate of change is ___________ (positive/negative/zero).
Q:
If the average rate of change is positive, then the function is ___________.
A) decreasing
B) increasing
C) not changing.
Q:
If the average rate of change is negative, then the function is ___________ (increasing/decreasing/not changing).
Q:
The graph below displays the population of the Madison, WI by decade. Find:
A) The total change from 1940 to 1980. Round answer to the nearest ten-thousand.
B) The average rate of change from 1940 to 1980. Round answer to 2 decimal places if necessary.
Q:
The graph below displays the population of the Madison, WI by decade. What would the units of the rate of change be?
A) People per thousand
B) Years per person
C) People per year
D) Years per thousand
Q:
A worker in a fast food restaurant earns a daily gross pay of $72.00 for 8 hours of work.
A) What is the pay rate, in dollars per hour? Round your answer to 2 decimal places.
B) How much will the worker earn for 33 hours of work?
C) How many hours will it take the worker to earn $5,500 in gross pay? Round your answer to the nearest hour.
Q:
In the first 8 years of his career, Hall of Fame baseball player Cal Ripken, Jr., had 1,180 base hits.
A) What was his average rate of hits per year for this eight-year period?
B) If he continued hitting at this same average rate, how many hits would he accumulate in the first 10 years of his career?
C) If he continued hitting at this same average rate, how long would it take him to get to 2,000 hits? Round to the nearest year.
Q:
The table below gives a girl's height (in inches) as a function of the child's age. Age (in years)
Girl's Height (in inches) 1
29.8 3
36.8 4
39.4 8
50.9 Use the data in the table and the average rates of change of height (in inches) to choose the best prediction for a girl's height (in inches) at age 10.
A) 56.84
B) 61.295
C) 53.87
D) 52.385
Q:
Find the average rate of change between data points A and B.
A: (13,5),
B: (-8,0),
C: (-3,-1),
D: (9,4).
Round your answer to 2 decimal places if necessary..
A) -0.24
B) 4.2
C) -5
D) 0.24
Q:
Find the average rate of change from data point C to data point B.
A: (2,3),
B: (-7,0),
C: (0,-5),
D: (-6,-6).
Round your answer to 2 decimal places if necessary..
Q:
The table below is a data set corresponding to the times achieved every 10 meters by Carl Lewis in the 100 meter final of the World Championships in Rome in 1987. Time (sec)
0.00
1.94
2.96
3.91
4.78
5.64
6.50
7.36
8.22
9.07
9.93 Distance (meters)
0
10
20
30
40
50
60
70
80
90
100 Over which of the following distance intervals was Carl Lewis's average speed the fastest?
A) from 60 meters to 90 meters
B) from 70 meters to 80 meters
C) from 20 meters to 40 meters
D) from 10 meters to 40 meters
Q:
The table below is a data set corresponding to the times achieved every 10 meters by Carl Lewis in the 100 meter final of the World Championships in Rome in 1987. Time (sec)
0.00
1.94
2.96
3.91
4.78
5.64
6.50
7.36
8.22
9.07
9.93 Distance (meters)
0
10
20
30
40
50
60
70
80
90
100 Find Carl Lewis's average speed (in meters per second) from the 70-meter mark to the 90-meter mark.
Round your answer to 2 decimal places.
A) 11.70
B) 0.09
C) 20
D) 25
Q:
The table below is a data set corresponding to the times achieved every 10 meters by Carl Lewis in the 100 meter final of the World Championships in Rome in 1987. Time (sec)
0.00
1.94
2.96
3.91
4.78
5.64
6.50
7.36
8.22
9.07
9.93 Distance (meters)
0
10
20
30
40
50
60
70
80
90
100 Find Carl Lewis's average speed (in meters per second) from the 30-meter mark to the 60-meter mark.
Round your answer to 2 decimal places.
Q:
The number of students enrolled in higher education in the state of Kentucky for the years from 1985 through 1992 is displayed in the following table. Year
1985
1986
1987
1988
1989
1990
1991
1992 Enrollment (in thousands)
80
82
85
91
95
105
106
110 Complete the sentence:
Between 1989 and 1992, the enrollment increased by an average of _________ students each year.
Round answers to 2 decimal places if necessary.
A) 15,000
B) 5,000
C) 0.2
D) 110,000
Q:
The number of students enrolled in higher education in the state of Kentucky for the years from 1985 through 1992 is displayed in the following table. Year
1985
1986
1987
1988
1989
1990
1991
1992 Enrollment (in thousands)
80
82
85
91
95
105
106
110 Complete the sentence:
Between 1986 and 1989, the enrollment increased by A)___________ students which is an average increase of B)___________ students per year.
Round answers to 2 decimal places if necessary.
Q:
The following table shows the number of new AIDS cases reported in Florida from 1986 to 1994. Year New AIDS Cases 1986
1031 1987
1633 1988
2650 1989
3448 1990
4018 1991
5471 1992
5086 1993
10958 1994
8617 Calculate the average annual rate of change of new AIDS cases per year from 1986 to 1994.
Round your answer to 2 decimal places, if necessary.
A) 0.11
B) 8,617
C) 948.25
D) 7,586
Q:
The following table shows the number of new AIDS cases reported in Florida from 1986 to 1994. Year New AIDS Cases 1986
1031 1987
1633 1988
2650 1989
3448 1990
4018 1991
5471 1992
5086 1993
10958 1994
8617 Calculate the average annual rate of change of new AIDS cases per year from 1988 to 1993.
Round your answer to 2 decimal places.
Q:
If a is measured in miles, b is measured in seconds, and c is measured in dollars, then find the units on the rate of change given by: A) dollars per second
B) dollars
C) seconds per dollar
D) seconds
Q:
A house valued at $65,000 in 1988 increased in value to $110,000 in 2001
A) What was the absolute change in value?
B) What was the average rate of change, in $ per year?
Round to 2 decimal places, if necessary.
Q:
The table shows the number of manatees killed by power boats in Florida from 1986 through 1990. Year
Manatees killed 1986
33 1987
39 1988
43 1989
50 1990
47 Find A) the total change in the number of manatees killed annually from 1987 to 1989 and
B) the average rate of change of the number of manatees killed annually from 1987 to 1989.
Round answers to 2 decimal places, if necessary.
Q:
The table below shows tobacco production in the United States for the years 1991-1996.
U.S. Tobacco Production: 1991-96 Year
Tobacco produced (millions of pounds) 1991
1664 1992
1722 1993
1613 1994
1583 1995
1269 1996
1565 A) Find the total change in tobacco production (in millions of pounds) from 1993 to 1995.
B) Determine by how many millions of pounds tobacco production has changed on average each year from 1993 to 1995.
Round answers to 2 decimal places, if necessary.
Q:
The table below gives population figures for Mexico for the period from 1980 to 1986.
Population of Mexico: 1980-1986 Year
Population (millions) 1980
67.38 1981
69.13 1982
70.93 1983
72.77 1984
74.66 1985
76.60 1986
78.95 Find A) by how many millions of people the population has increased from 1980 to 1985 and
B) by how many millions of people the population has increased on average each year from 1980 to 1985.
Round answers to 2 decimal places, if necessary.
Q:
The table below gives the life expectancy of a child (at birth) in the United States for selected years from 1920 to 1990.
(Source: Department of Health and Human Services) Year
1920
1930
1940
1950
1960
1970
1980
1990 Life expectancy
54.1
59.7
62.9
68.2
69.7
70.8
73.7
75.4 Complete the sentence:
Between 1930 and 1940, the life expectancy of a child increased by A)___________ years of life which is an average increase of B)___________ years of life expectancy each year.
Round answers to 2 decimal places if necessary.
Q:
Use technology to graph the function and then determine the interval over which the function is decreasing. State your answer in interval notation.
y = x3 - 3x
Q:
Use technology to graph the function and then determine the interval over which the function is increasing. State your answer in interval notation.
y = x3 - 48x
Q:
Use technology to graph the function and then determine the interval over which the function is decreasing. State your answer in interval notation.
y = x4 - 8x2
Q:
Use technology to graph the function and then determine the interval over which the function is increasing. State your answer in interval notation.
y = 5x4 - 40x2
Q:
Use technology to graph the function and then determine the interval on which the graph is concave downward. State your answer in interval notation.
y = 4.75x4 - 114x2
Q:
Use technology to graph the function and then determine the interval on which the graph is concave upward. State your answer in interval notation.
y = 3.5x4 - 21x2
Q:
Use technology to graph the function and then determine the interval on which the graph is concave downward. State your answer in interval notation.
y = 5x3 - 3x
Q:
Use technology to graph the function and then determine the interval on which the graph is concave upward. State your answer in interval notation.
y = x3 - 3x
Q:
Given the graph of velocity as a function of time, choose the best graph to represent distance traveled as a function of time. A) B) C) D)
Q:
Use the graph of y = f(x) to find f(-1).
Q:
Determine the range of this graph. Express the answer in interval notation.
Q:
Determine the domain of this graph. Express the answer in interval notation.
Q:
The graph below shows the number of birds at a bird feeder as a function of time. What event most likely occurred during interval E?
A) A cat chases all the birds away.
B) Birds are coming back after being chased away by a cat.
C) The feeder is full of birds and there is no room for more.
D) The feeder was still empty from the previous day.
Q:
Identify the minimum of this function over the interval shown.
Q:
Identify the maximum of this function over the interval shown.
Q:
State the interval on which this graph is concave upward. State your answer in interval notation.
Q:
State the interval on which this graph is concave downward. State your answer in interval notation.
Q:
On what interval is this graph decreasing. State your answer in interval notation.
Q:
On what interval is this graph increasing. State your answer in interval notation.
Q:
On what interval is this graph decreasing. State your answer in interval notation.
Q:
On what interval is this graph increasing. State your answer in interval notation.
Q:
If the tank pictured here is filled with a pipe flowing at a constant rate, sketch the graph of the height of the water in the tank as a function of time.
Q:
Each of these tanks is being filled with a pipe that delivers 6 gallons of water per minute. Which graph best represents the height of the water in each tank as a function of time? A) B) C) D)
Q:
Which graph most likely illustrates the average daily temperature as a function of time (in months).
Assume the horizontal axis represents time.
A) B) C) D)
Q:
Over what interval is the function concave down?
Write your answer in interval notation.