Download worksheet - domains and ranges of relations

Name: - - - - - - - - - - - - - - - - -
Per: - - -Date: - - - - - - - -
WORKSHEET - DOMAINS AND RANGES OF
RELATIONS AND FUNCTIONS
Part 1 - Identify Domains, Ranges, and Functions. Identify the domain and range of
each relation given below. Then determine if the relation represents a function.
Record your answers in the appropriate spaces provided for each problem.
1. {(2, 3), (-1,5), (0, -1), (3,5), (5, O)}
Domain: - - - - - - - - - - Range:
_
Function:
2.
yes
no
3.
x
y
y
Domain: - - - - - - - - - -
Domain:
- - - - - - - - - - - -
Range:
Range:
_
Function:
4.
x
yes
~
no
yes
Function:
5.
II'
--'--no
"
-
_... ­
_
• •
-­
~
~
Bl
~
!
_01--,--,.-­
~
I
I
j
'-'­
..
Domain: - - - - - - - - - - - ­
Domain: - - - - - - - - - ­
Range:
Function:
_
yes
no
Range:
Function:
_
yes
no
Name:
Per:
Date: - - - - - - - -
Part 2 - Different Representations. Read each problem carefully and perform the
indicated task. Also, for each problem, determine if the relation given. represents a
function and record your answers in the appropriate spaces provided for each
problem.
6. Rewrite the relation given to the right as a set of
ordered pairs.
Answer:
Function:
yes
no
7. Graph the relation given below on the coordinate plane to the right.
Function:
yes
no
I
8. Construct a mapping diagram in the space below to represent the following set of ordered pairs.
(2, -1), (3, 2), (5,4), (3, -1), (6,5)
Mapping diagram:
Function:
yes
no
9. Create a table that is equivalent to the relation graphed on the
coordinate plane to the right.
•
llr.
•
Table:
I
I
- +=
-- I-­
Function:
yes
no
,­
Complete the table of solutions for each equation. Then
graph the solutions and draw a line through them. The line,
if extended, will cross a letter outside the grid. Write this
letter in each box containing the exercise number.
4
1
3
'I
6
5
2
4
I
E
\V
'v
~
,~
y = 3x - 1
y
v
y
x
=:
-2x
X
+
3
Y
u
5
3
Ix
X
2
-3
A
-2
c
2
0
0
s
R
\\1
.,
~
'v
•
"''' y
= -x - 2
x
H
y
T
y == ~x
x
+
4
y
4
6
x
Ix
-5
6
D
-2
-2
0
0
o
F
N
'v
.,
.A
~,
Y;=-~X+ 1
y = 7 - 2x
x
y
\V
X
B
Ix
X
-1
-6
5
3
Functions and Linear Equations and Inequalities:
Linear Equations
Y
6
2
0
G
s
0
10,,5
L
PUNCHLINE • Bridge to Algebra • 2nd Ed.
©2009 Marcy Mathworks
1 What function is represented by
the following table?
A Y = -x
B
c
D
x
y
-2
6
0
4
2
2
4 Which table of ordered pairs
represents a function with the
following rule?
y=4x-ll
x
F
+4
y=4x+l
y = -3x
y = -x - 4
-
2 What is the range of the relation
represented below?
H
[{-S, 8), (-3,2) (6, 10), (10, 8)}l
G
H
J
{-S, -3, 6, lOl
{8,lOl
{2, 8, lOl
16,lO}
J
3 Jed's Canoe Rental uses the
function c = Sh + 10 to calculate
the cost, c, of renting a canoe for
h hours. Which statement is
true?
A
B
C
D
y
0
11
1
15
2
19
·x
0
y
7··
G
F
-
The independent variable is h.
The independent variable is c.
Both variables are independent.
Both variables are dependent.
-99­
1
-7
5
9
10
27
··x
y
2
-3
4
-5
6
-13
··x·
y
3
1
5
9
7
17
7 Which equation represents the
rule for the function shown in
the table below?
Directions: Use the following
information to answer Numbers
5 and 6.
The Chavez family went on vacation.
The following table shows the
distances they traveled in the first
four hours.
Time
(in hours)
Distance
(in miles)"
1
52
2
104
3
156
4
208
5 Which is the equation that
represents the information
above? Let d = the distance and
t = the time elapsed.
A
B
c
. D
d = t + 52
d = 52t
d = 52t + 52
d = 52 + 2t
G
H
J
520
468
416
260
y
2
6
4
7
6
8
A
y=2x+6
B
y=x+4
C
Y
=
1
-x + 5
2
D
Y
=
2x - 10
8 What is domain of the relation
represented by the table below?
6 If they continued to travel at the
Sanle rate the entire trip, how
many miles would the Chavez
family travel in 9 hours?
F
x
miles
miles
miles
miles
x
y
-9
45
-6
30
-3
15
0
0
~
-.J
3
-15
r
CD
z
6
-30
o
9
-45
w
o
iii
rt:
o
lL
~
(CJ
G
{-45, -30, -15, 0, 15,30, 45}
{-g, -6, -3, 0, 3, 6, g}
H
{O, 3, 6, g}
J
{15, 30, 45}
F
z
>=
11.
o
()
ci>
c
:c.!!l
:0
:J
11.
c
~
o
Q)
31
o
:J
CD
co
o
~
@
-100­
(
lomain
x-Coordinate
x-Axis
x-Intercept
Dependent Variable
<.ange
~-Coordinate
~-Axis
~-Intercept
Independent Variable
Linear E9uatlon
Quadrants
Ordered Pair
Origin
Coordinate Plane
Relation
Function
1) The set of outputs of a function, the set ofV numbers.
1)
_
2) An equation whose graph is a line.
2) - - _ . _ - - - - - ­
3) Horizontal line dividing the coordinate plane into positive and negative y.
3)
_
4) The point at which the x-axis and v-axis intersect.
4)
_
5) The first number in an ordered pair.
5)
_
6) Set of ordered pairs such as {(2, 3L {-2/ OL {O/ 5L (-4/ -6)}.
6)
_
7) Relation in which each member in the domain is paired with exactlv one
7)
_
The variable for the output of a function.
8)
_
9) The point at which a line crosses the v-axis.
9)
_
member in the range.
~o)
10) A 2-dimensional grid with an x-axis and a v-axis.
10)
11) The set of inputs of a function; the set of x values.
11)
_
12) The variable for the input of a function.
12)
_
13) The second number in an ordered pair.
13)
_
14) The coordinate plane is divided into 4 ofthese sections.
14)
15) The point at which a line crosses the x-axis.
15)
_
16) 2 numbers; the first is the x-coordinate and the second is the v-coordinate. 16)
_
17) Vertical line dividing the c.oordinate plane into positive and negative x.
_
17)
_
_