Chapter 1.4, Problem 9E

a .

To determine

To find: if the set of ordered pairs $\left\{\left(0,1\right),\left(1,-2\right),\left(2,0\right),\left(3,2\right)\right\}$ represents function from $A=\left\{0,1,2,3\right\}$ to $B=\left\{-2,-1,0,1,2\right\}$ .

Answer to Problem 9E

Function

Explanation of Solution

Concept Used:

Function: A function is a relation which maps each element belonging to set A to exactly one element belonging to the set B.

The given set of ordered pairs $\left\{\left(0,1\right),\left(1,-2\right),\left(2,0\right),\left(3,2\right)\right\}$ represents a function because each element in set $A=\left\{0,1,2,3\right\}$ is assigned to exactly one element of set $B=\left\{-2,-1,0,1,2\right\}$ .

b.

To determine

To find: if the set of ordered pairs $\left\{\left(0,-1\right),\left(2,2\right),\left(1,-2\right),\left(3,0\right),\left(1,1\right)\right\}$ represents function from $A=\left\{0,1,2,3\right\}$ to $B=\left\{-2,-1,0,1,2\right\}$ .

Answer to Problem 9E

Not a function

Explanation of Solution

Concept Used:

Function: A function is a relation which maps each element belonging to set A to exactly one element belonging to the set B.

The given set of ordered pairs $\left\{\left(0,-1\right),\left(2,2\right),\left(1,-2\right),\left(3,0\right),\left(1,1\right)\right\}$ is not a function because the element 1 belonging to the set $A=\left\{0,1,2,3\right\}$ is assigned to two elements ‘1’ and ‘2’ in the set $B=\left\{-2,-1,0,1,2\right\}$ .

c .

To determine

To find: if the set of ordered pairs $\left\{\left(0,0\right),\left(1,0\right),\left(2,0\right),\left(3,0\right)\right\}$ represents function from $A=\left\{0,1,2,3\right\}$ to $B=\left\{-2,-1,0,1,2\right\}$ .

Answer to Problem 9E

Function

Explanation of Solution

Concept Used:

Function: A function is a relation which maps each element belonging to set A to exactly one element belonging to the set B.

The given set of ordered pairs $\left\{\left(0,0\right),\left(1,0\right),\left(2,0\right),\left(3,0\right)\right\}$ represents a function because each element in set $A=\left\{0,1,2,3\right\}$ is assigned to exactly one element of set $B=\left\{-2,-1,0,1,2\right\}$ .

d.

To determine

To find: if the set of ordered pairs $\left\{\left(0,2\right),\left(3,0\right),\left(1,1\right)\right\}$ represents function from $A=\left\{0,1,2,3\right\}$ to $B=\left\{-2,-1,0,1,2\right\}$ .

Answer to Problem 9E

Not a function

Explanation of Solution

Concept Used:

Function: A function is a relation which maps each element belonging to set A to exactly one element belonging to the set B.

The given set of ordered pairs $\left\{\left(0,2\right),\left(3,0\right),\left(1,1\right)\right\}$ is not a function because there is an element 1 belonging to the set $A=\left\{0,1,2,3\right\}$ which is not assigned to any element in the set $B=\left\{-2,-1,0,1,2\right\}$ .