Functions Review
Date:
Name:
1.
John left his home and walked 3 blocks to his school, as shown in
the accompanying graph.
3.
The accompanying graph represents the yearly cost of playing 0 to
5 games of golf at the Shadybrook Golf Course. What is the total
cost of joining the club and playing 10 games during the year?
4.
Which equation could represent the relationship between the x and y
values shown in the accompanying table?
What is one possible interpretation of the section of the graph from
point B to point C?
(1) John arrived at school and stayed throughout the day.
(2) John waited before crossing a busy street.
(3) John returned home to get his mathematics homework.
(4) John reached the top of a hill and began walking on level ground.
2.
During a 45-minute lunch period, Albert (A) went running and
Bill (B) walked for exercise. Their times and distances are shown in
the accompanying graph. How much faster was Albert running than
Bill was walking, in miles per hour?
x
y
0
2
2
6
1
3
3
11
4 18
(1) y = x + 2
5.
(2) y = x2 + 2
(3) y = x2
(4) y = 2x
If x and y are de ned as indicated by the accompanying table, which
equation correctly represents the relationship between x and y?
x
y
2
1
5
7
3
3
7 11
(1) y = x + 2
page 1
(2) y = 2x + 2
(3) y = 2x + 3
(4) y = 2x
3
6.
The accompanying graph shows the amount of water left in Rover's
water dish over a period of time.
8.
Super Painters charges $1.00 per square foot plus an additional fee of
$25.00 to paint a living room. If x represents the area of the walls of
Francesca's living room, in square feet, and y represents the cost, in
dollars, which graph best represents the cost of painting her living
room?
(1)
How long did Rover wait from the end of his rst drink to the start
of his second drink of water?
(1) 10 sec
7.
(2) 30 sec
(3) 60 sec
(2)
(4) 75 sec
Which linear equation represents the data in the accompanying table?
c
d
0
20.00
2
23.00
1
3
21.50
24.50
(1) d = 1:50c
(2) d = 1:50c + 20:00
(3) d = 20:00c + 1:50
(4) d = 21:50c
(3)
(4)
page 2
Functions Review
9.
The population growth of Boomtown is shown in the accompanying
graph.
11.
Granola bars cost $0.55 each. Which table represents this relationship?
(1)
(2)
(3)
If the same pattern of population growth continues, what will the
population of Boomtown be in the year 2020?
(1) 20,000
10.
(2) 32,000
(3) 40,000
(4) 64,000
(4)
Which equation expresses the relationship between x and y, as shown
in the accompanying table?
x 0 1 2
3
y 2 5 8 11
(1) y = x + 3
4
14
(2) y = 2x + 3
(3) y = 3x + 2
(4) y = x + 2
12.
page 3
A bug travels up a tree, from the ground, over a 30-second interval.
It travels fast at rst and then slows down. It stops for 10 seconds,
then proceeds slowly, speeding up as it goes. Which sketch best
illustrates the bug's distance (d) from the ground over the 30-second
interval (t)?
(1)
(2)
(3)
(4)
Functions Review
13.
Antwaan leaves a cup of hot chocolate on the counter in his kitchen.
Which graph is the best representation of the change in temperature
of his hot chocolate over time?
14.
In a science ction novel, the main character found a mysterious rock
that decreased in size each day. The table below shows the part of
the rock that remained at noon on successive days.
(1)
Day
Fractional Part of
the Rock Remaining
1
1
1
2
1
4
1
8
2
3
4
Which fractional part of the rock will remain at noon on day 7?
(1)
(2)
15.
1
128
(2)
Side Length Area of
of a Square Square
1
14
1
12
(4)
(3)
(3)
(2)
Hours
Worked
2
4
20
4
16
30
Pay
$160
9
25
$200
5
25
35
$280
Age
Group
Frequency
20–29
40–49
3
30–39
50–59
$240
People
Number of
Fingers
9
2
20
10
4
40
(4)
7
3
4
30
5
50
Which table does not show bivariate data?
(1)
(4)
Height
(inches)
Weight
(pounds)
39
50
60
90
48
(3)
(2)
Gallons
15
20
70
25
Quiz
Average
Frequency
70
12
40
90
6
55
80
page 4
(3)
Which data table represents univariate data?
(1)
16.
1
64
15
(4)
Speed
(mph)
50
Miles
Driven
300
400
500
Distance
(miles)
80
120
150
Functions Review
17.
Four hundred licensed drivers participated in the math club's survey
on driving habits. The table below shows the number of drivers
surveyed in each age group.
20.
Ages of People in
Survey on Driving Habits
Age Group
16–25
Which diagram shows a relation that is not a function?
(1)
(2)
(3)
(4)
Number of
Drivers
150
26–35
129
46–55
57
36–45
33
56–65
31
Which statement best describes a conclusion based on the data in
table?
(1) It may be biased because no one younger than 16 was surveyed.
21.
(2) It would be fair because many di erent age groups were surveyed.
(3) It would be fair because the survey was conducted by the math
club students.
Which graph of a relation is also a function?
(1)
(2)
(3)
(4)
(4) It may be biased because the majority of drivers surveyed were
in the younger age intervals.
18.
19.
Which graph represents a function?
(1)
(2)
(3)
(4)
Which diagram is not the graph of a function?
(1)
(2)
(3)
(4)
page 5
Functions Review
22.
Which graph does not represent a function?
23.
(1)
Which graph does not represent a function of x?
(1)
(2)
(2)
(3)
(3)
(4)
(4)
page 6
Functions Review
24.
Each graph below represents a possible relationship between
temperature and pressure. Which graph does not represent a function?
26.
Which graph represents a linear function?
(1)
(1)
(2)
(2)
(3)
(3)
(4)
(4)
25.
The accompanying graph shows the curves of best t for data points
comparing temperature to altitude in four di erent regions, represented
by the relations A, B, C, and D.
Which relation is not a function?
(1) A
(2) B
(3) C
(4) D
page 7
Functions Review
27.
Which statement is true about the relation shown on the graph below?
29.
(1) It is a function because there exists one x-coordinate for each
y-coordinate.
The graph of y = f (x) is shown below.
Which set lists all the real solutions of f (x) = 0?
(2) It is a function because there exists one y-coordinate for each
x-coordinate.
(1) f 3; 2g
(3) It is not a function because there are multiple y-values for a
given x-value.
(2) f 2; 3g
(3) f 3; 0; 2g
(4) f 2; 0; 3g
(4) It is not a function because there are multiple x-values for a
given y-value.
28.
Which type of function is graphed below?
(1) linear
(2) quadratic
(3) exponential
(4) absolute value
page 8
Functions Review
30.
Which graph represents a function?
32.
(1)
33.
Which relation is also a function?
(1) x2 + y2 = 36
(2) x2
(3) 9x2 + 4y2 = 36
(4) y = 4x2
Which equation does not represent a function?
(2) y = x2
(1) y = 4
(3) y = x
34.
(2)
36.
(3)
37.
38.
31.
(4) x2 + y2 = 4
4
(1) y = 2x
(2) y = x2 + 10
10
x
(4) x2 + y2 = 9
Which relation is not a function?
(1) y = 2x + 4
(2) y = x2
(3) x = 3y
(4) x = y2 + 2x
2
4x + 3
3
Which relation is a function?
(1) xy = 7
(2) x = 7
(3) x2
(4) x2 + y2 = 7
y2 = 7
Given the relation R = f( 2; 3); (a; 4); (1; 9); (0; 7)g. Which
placement for a makes this relation a function
(1) 1
(4)
4
Which equation does not represent a function?
(3) y =
35.
y2 = 36
(2)
2
(3) 0
(4) 4
Which function is not one to one?
(1)
(2)
(3)
(4)
Which relation is also a function?
(1) x2 + y2 = 64
(2) x4 + 4y2 = 64
(3) x2
(4) xy = 64
4y2 = 64
page 9
Functions Review
39.
Which diagram represents a one-to-one function?
(1)
(2)
45.
If f (x) = 2x2 + 6, nd the value of f ( 3).
46.
If f (x) = x2 + 3x
47.
If f (x) = x3
5, nd the value of f (3).
3 , then f ( 1) is equivalent to
(1) 0
(3)
40.
41.
(4)
(2) 2
2
(4) 4
48.
Given the function: f (x) = (x + 1)2 . What is the value of f ( 2)?
49.
If f (x) =
50.
If f (b) = b0 + b
51.
What is the domain of the function f (x) = p
p
25
x2 , nd the value of f (3).
1
+ b 2 , nd f (2).
4
x+1
over the set of real
Which set of ordered pairs is not a function?
numbers?
(1) f(3; 1); (2; 1); (1; 2); (3; 2)g
(2) f(4; 1); (5; 1); (6; 1); (7; 1)g
(1) fx j x = 1g
(2) fx j x
(3) f(1; 2); (3; 4); (4; 5); (5; 6)g
(4) f(0; 0); (1; 1); (2; 2); (3; 3)g
(3) fx j x < 1g
(4) fx j x > 1g
On the accompanying diagram, draw a mapping of a relation from
set A to set B that is not a function. Explain why the relationship
you drew is not a function.
52.
What is the domain of the function f (x) =
(1)
xjx
(3)
xjx
3
7
3
7
Which set of ordered pairs does not represent a function?
(2) f(3; 2); (3; 4); (4; 1); (4; 3)g
3x + 7 ?
(2)
xjx
(4)
xjx
7
3
7
3
A function is de ned by the equation y = 8x 3. If the domain is
2 x 4, nd the minimum value in the range of the function.
54.
The domain of the function f (x) = p
55.
(1) f(3; 2); ( 2; 3); (4; 1); ( 1; 4)g
p
1g
53.
(1) fx j x 6= 1g
42.
(3)
(2) fx j x
The domain for f (x) = x2
range of f (x) is
(1) 0
(2) 16
1g
3 is 0
3
x
1
is
(3) fx j x < 1g
(4) fx j x > 1g
x < 4. The smallest value in the
(3)
3
(4) 4
(3) f(3; 2); (4; 3); (5; 4); (6; 5)g
(4) f(3; 2); (5; 2); (4; 2); ( 1; 2)g
43.
Given the relation f(8; 2); (3; 6); (7; 5); (k; 4)g, which value of k
will result in the relation not being a function?
(1) 1
44. If f (x) = 3
(2) 2
(3) 3
(4) 4
x2 , nd f ( 2).
page 10
Functions Review
56.
Which graph illustrates a quadratic relation whose domain is all real
numbers?
(1)
63.
Which diagram represents a relation in which each member of the
domain corresponds to only one member of its range?
(1)
(2)
(2)
(3)
57.
(4)
The domain of the equation y =
(x
1
1)2
is all real numbers
(1) greater than 1
(2) except 1
(3) less than 1
(4) except 1 and
1
3
58.
Which negative real number is not in the domain of
59.
In the set of real numbers, what is the domain of f (x) =
(1) x
60.
5
(3) x > 5
(2) f2g
(3) f2; 2g
If the domain of f (x) = 2x + 3 is f 3 < x
in the range?
(1)
62.
5
x2
4
p
?
x + 5?
(4)
(4) x > 0
If the domain is the set of real numbers, what is the solution set for
the equation x2 + 4 = 0?
(1) f 2g
61.
(2) x
(3)
1
(2) 0
(4) fg
0g, which number is not
(3) 3
(4) 6
What is the domain of f (x) = 2x ?
(1) all integers
(2) all real numbers
(3) x
(4) x
0
0
page 11
Functions Review
64. The accompanying graph shows the heart rate, in beats per minute, of
a jogger during a 4-minute interval.
66.
The e ect of pH on the action of a certain enzyme is shown on the
accompanying graph.
What is the domain of this function?
(1) 4
What is the range of the jogger's heart rate during this interval?
(1) 0–4
65.
(2) 1–4
(3) 0–110
(4) 60–110
67.
13
x
(2) 4
y
13
(3) x
0
(4) y
0
Data collected during an experiment are shown in the accompanying
graph.
The pro t, P, for manufacturing a wireless device is given by the
equation P = 10x2 + 750x 9;000, where x is the selling price, in
dollars, for each wireless device. What range of selling prices allows
the manufacturer to make a pro t on this wireless device? [The use
of the grid below is optional.]
What is the range of this set of data?
(1) 2:5
(3) 0
page 12
y
y
9:5
100
(2) 2:5
(4) 1
x
x
9:5
10
Functions Review
68.
A meteorologist drew the accompanying graph to show the changes in
relative humidity during a 24-hour period in New York City.
70.
The accompanying graph illustrates the presence of a certain strain of
bacteria at various pH levels.
What is the range of this set of data?
(1) 0
(3) 30
69.
24
y
y
(2) 0
80
(4) 30
What is the range of this set of data?
24
x
x
(1) 5
80
71.
The accompanying graph shows the elevation of a certain region in
New York State as a hiker travels along a trail.
x
9
(2) 5
x
70
(3) 0
70
y
(4) 5
y
70
The air temperature in Dallas, Texas, over a 5-hour period is shown
in the accompanying graph.
What is the domain of this function?
(1) 1;000
x
(3) 0
12
x
1;500
(2) 1;000
y
(4) 0
12
y
1;500
What is the range of this set of data?
page 13
(1) 0
x
5
(2) 56
x
70
(3) 0
y
80
(4) 56
y
70
Functions Review
72.
What are the domain and the range of the function shown in the
graph below?
75.
What is the range of the function shown below?
(1) x
73.
74.
(1) fxjx > 4g; fyjy > 2g
(2) fxjx
(3) fxjx > 2g; fyjy > 4g
(4) fxjx
What is the range of f (x) = jx
4g; fyjy
2g; fyjy
76.
2g
4g
0
(2) x
0
(3) y
0
(4) y
0
The graph below shows the average price of gasoline, in dollars, for
the years 1997 to 2007.
3j + 2?
(1) fxjx
3g
(2) fyjy
2g
(3) fxjx
real numbersg
(4) fyjy
real numbersg
What is the domain of the function shown below?
What is the approximate range of this graph?
(1)
1
x
6
(2)
1
y
6
(3)
2
x
5
(4)
2
y
(1) 1997
x
2007
(2) 1999
x
2007
(3) 0:97
y
2:38
(4) 1:27
y
2:38
5
page 14
Functions Review
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Functions Review
04/29/2015
1.
Answer:
2
21.
Answer:
2
2.
Answer:
4
22.
Answer:
4
3.
Answer:
$390
23.
Answer:
1
4.
Answer:
2
24.
Answer:
3
5.
Answer:
4
25.
Answer:
1
6.
Answer:
2
26.
Answer:
1
7.
Answer:
2
27.
Answer:
3
8.
Answer:
3
28.
Answer:
3
9.
Answer:
2
29.
Answer:
4
10.
Answer:
3
30.
Answer:
1
11.
Answer:
2
31.
Answer:
4
12.
Answer:
3
32.
Answer:
4
13.
Answer:
1
33.
Answer:
4
14.
Answer:
2
34.
Answer:
4
15.
Answer:
3
35.
Answer:
4
16.
Answer:
3
36.
Answer:
1
17.
Answer:
4
37.
Answer:
4
18.
Answer:
4
38.
Answer:
2
19.
Answer:
1
39.
Answer:
3
20.
Answer:
1
40.
Answer:
1
Teacher's Key
41.
Answer:
[task]
63.
Answer:
3
42.
Answer:
2
64.
Answer:
4
43.
Answer:
3
65.
Answer:
15 < x < 60
1
44.
Answer:
1
66.
Answer:
45.
Answer:
12
67.
Answer:
3
13
68.
Answer:
3
47.
Answer:
4
69.
Answer:
3
48.
Answer:
1
70.
Answer:
4
49.
Answer:
4
71.
Answer:
4
50.
Answer:
1 34
72.
Answer:
2
73.
Answer:
2
74.
Answer:
1
75.
Answer:
3
76.
Answer:
3
46.
Answer:
51.
Answer:
4
52.
Answer:
2
53.
Answer:
13
54.
Answer:
4
55.
Answer:
3
56.
Answer:
3
57.
Answer:
2
58.
Answer:
2
59.
Answer:
1
60.
Answer:
4
61.
Answer:
4
62.
Answer:
2
Page 2