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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) _