----------------- --- --------
-----------
---------- ------------
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: yes no
2. x
y
3. x
y
Domain: Domain:
Range: _ Range: --'--- _
Function: yes no Function: yes no
5.4.
~ II' _...
• •
Bl !
~ _01--,---,.-I I
j ..
-
- " -
~
~ ~
'-'
Domain: --------- Domain: -----------
Range: _ Range: _
Function: yes no 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.
Table:
• llr.
• I
I
- +=
--I-
Function: yes no
c
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.
E I
,4 3 1 'I 6 5 2 4
y = 3x - 1
x y
3
2
-2
0
\V
~ ,~
v u
X
A
y =: -2x + 3
X Y
5
-3
2
0
'v
Ix
R s \\1 'v
~
= -x - 2
x y
6
-5
-2
0
T "''' y
H
Ix D
•., y == ~x + 4
x y
4
6
-2
0 o
F N
.A 'v
Ix
Y;=-~X+ 1
X Y
6
-6
3
0
Gy = 7 - 2x
x y
2
-1
5
0
.,~,
B
s
Functions and Linear Equations and Inequalities: PUNCHLINE • Bridge to Algebra • 2nd Ed. Linear Equations 10,,5 ©2009 Marcy Mathworks
\V
X
x
L
1 What function is represented by the following table?
x y
-2 6
0 4
2 2
A Y = -x + 4
B y=4x+l
c y = -3x
D y = -x - 4
2 What is the range of the relation represented below?
[{-S, 8), (-3,2) (6, 10), (10, 8)}l
F {-S, -3, 6, lOl
G {8,lOl H {2, 8, lOl J 16,lO}
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 The independent variable is h.
B The independent variable is c.
C Both variables are independent.
D Both variables are dependent.
4 Which table of ordered pairs represents a function with the following rule?
y=4x-ll
x - y
0 11
1 15
2 19
-7··
·x 0
y
1 -7
5 9
10 27
-99
F
G
··x
2 H
4
6
J
y -3
-5
-13
··x· y
3 1
5 9
7 17
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 Distance (in hours) (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 d = t + 52
B d = 52t
c d = 52t + 52 . D d = 52 + 2t
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 520 miles
G 468 miles
H 416 miles
J 260 miles
7 Which equation represents the rule for the function shown in the table below?
x y
2 6
4 7
6 8
A y=2x+6
B y=x+4
1 C Y = -x + 5
2
D Y = 2x - 10
8 What is domain of the relation represented by the table below?
F
G
H
J
-100
x y
-9 45
-6 30
-3 15
0 0
3 -15
6 -30
9 -45
~ -.J
r CD z w o o iii rt: o lL
~ (CJ z
{-45, -30, -15, 0, 15,30, 45} >=11. o
{-g, -6, -3, 0, 3, 6, g} ()
ci>
{O, 3, 6, g} :cc
.!!l :0
{15, 30, 45} :J 11. c ~ o Q)
31 o :J
CD co o ~ @
(
lomain x-Coordinate x-Axis x-Intercept Dependent Variable
Independent Variable<.ange ~-Coordinate ~-Axis ~-Intercept
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) _
member in the range.
~o) The variable for the output of a function. 8) _
9) The point at which a line crosses the v-axis. 9) _
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) _