MULTIPLE REPRESENTATION OF RELATIONS WORKSHEET

Express the relation as

i) set of ordered pairs

ii) Table

iii) Graph

iv) mapping diagram

Problem 1 :

In the scoring of some track meets, for 1st place you get 5 points, for 2nd place you get 3 points, for 3rd place you get 2 points and for 4th place you get 1 point.

Solution

Problem 2 :

g(m) = m2

for the domain {-2, 0 2}

Solution

Problem 3 :

h(x) = -1/3x – 1

for the domain {-3, 0, 6}

Solution

Problem 4 :

A tanning salon charges a one – time maintenance fee of $12 plus $4 for each tanning visit. Write a function to describe the situation. Find a reasonable domain and range for the function for up to 6 visits.

Solution

Problem 5 :

f(x) = x2 + x – 2

for the domain {-2, 0 1}

Solution

Answer Key

1)

a)  {(1, 5), (2, 3), (3, 2), (4, 1)}

b) 

           Place

                     1           

                 2         

         3

       4

Points

5

3

2

1

c)

mulrepofrel1

d)

gra-h6

2)  m = -2, g(-2) = 4, m = 0, g(0) = 0, m = 2, g(2) = 4

a) Set of ordered pairs is

{(-2, 4), (0, 0), (2, 4)}.

b) Table of values :

g(m)

g(-2)

g(0)

g(2)

m2

4

0

4

c) Graph

mulrepofrel9

d) Mapping diagram

mapdia

3)  x = -3, h(-3) = 0, x = 0, h(0) = -1, x = 6, h(6) = -3

a)  Set of ordered pairs is

{(-3, 0), (0, -1), (6, -3)}.

b) Table

h(x)

h(-3)

h(0)

h(6)

-1/3x - 1

0

-1

-3

c) Graph

mulrepofrel3

d) Mapping diagram 

mapdia2

4)  y = 12 + 4x

0 ≤ x ≤ 6 and x should be an integer.

x = 0, y = 12, x = 1, y = 16, x = 2, y = 20

x = 3, y = 24, x = 4, y = 28, x = 5, y = 32

x = 6, y = 36

domain = {0, 1, 2, 3, 4, 5, 6}.

Range = {12, 16, 20, 24, 28, 32, 36}

a. Set of ordered pairs :

{(0, 12), (1, 16), (2, 20), (3, 24), (4, 28), (5, 32), (6, 36)}.

b) Table :

x

0

1

2

3

4

5

6

y

12

16

20

24

28

32

36

c) Graph :

mulrepofrel4

d)  Mapping Diagram :

mulrepofrel5

5)  x = -2, f(-2) = 0, x = 0, f(0) = -2, x = 1, f(1) = 0

range = {-2, 0}

a. Set of ordered pairs :

{(-2, 0), (0, -2), (1, 0)}.

b. Table :

f(x)

f(-2)

f(0)

f(1)

x2 + x - 2

0

-2

0

c. Graph :

mulrepofrel6

d. Mapping Diagram :

mulrepofrel8

Express the relation as

i)  a table

ii) a graph

iii)  a mapping

Then, state the domain and range of the relation. 

Problem 1 :

{(-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3)}

Solution

Problem 2 :

{(-3, -3), (-1, 1), (0, 2), (2, -3), (2, 3)

Solution

Problem 3 :

{(-1, -1), (1, 1), (2, 1), (3, 2)}

Solution

Problem 4 :

{(3, -2), (1, 0), (-2, 4), (3, 1)}

Solution

Problem 5 :

{(0, 4), (-4, -4), (-2, 3), (4, 0)}

Solution

Answer Key

1)

a)

x

-2

-1

1

2

4

y

1

0

2

-4

3

Graph :

graph1

Mapping a diagram :

expressingfuncindifferentform

Domain = {-2, -1, 1, 2, 4}

Range :

{1, 0, 2, -4, 3}

2)  Table :

If x = -3 and y = -3

x = -1 and y = 1

x = 0 and y = 2

x = 2 and y = -3

x = 2 and y = 3

Graph :

graph2
expressrelationindifferentformq3

Domain :

{-3, -1, 0, 2}

Range :

{-3, 1, 2, 3}

This relation is not a function.

3)  

Table :

If x = -1 and y = -1

x = 1 and y = 1

x = 2 and y = 1

x = 3 and y = 2

Graph :

graph31

Mapping a diagram :

expressrelationindifferentformq4

Domain :

(-1, 1, 2, 3)

Range :

(-1, 1, 2)

4)  

Table :

If x = 3 and y = -2

x = 1 and y = 0

x = -2 and y = 4

x = 3 and y = 1

Graph :

graph4

Mapping a diagram :

Map41

Domain :

{3, 1, -2}

Range :

{-2, 0, 4, 1}

5)  

Table :

If x = 0 and y = 4

x = -4 and y = -4

x = -2 and y = 3

x = 4 and y = 0

Graph :

graph5

Mapping a diagram :

Map5

Domain :

{0, -4, -2, 4}

Range :

{-4, 0, 3, 4}

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