Chapter 2, Problem 2RE

To determine

Whether the given relation represents a function. Also find the domain and range.

Answer to Problem 2RE

The given relation does not represent a function.

Explanation of Solution

Given information:

A set of relation is given as

  $\left\{\left(4,-1\right),\left(2,-1\right),\left(4,2\right)\right\}$

Concept used:

Consider two sets A and B . If each element $x$ in the set A has exactly one element $y$ in the set B , the relation between them is known as a function.The ordered pair is $\left(x,y\right)$ .

The values of first coordinate $x$ is known as input values and the values of second coordinate $y$ is known as output values of a function.

For each random value of $x$ , the variable $y$ will give a different value.

The set of input values represent the domain and set of output values represent the range of the function.

The set of all images of the elements in the domain of a function is defined as the range of the function.

The set of all first elements of each ordered pair is the domain.

The set of all second elements of each ordered pair is the range.

Calculation:

Consider the given set of relation.

  $\left\{\left(4,-1\right),\left(2,-1\right),\left(4,2\right)\right\}$

The ordered pair $\left(4,-1\right)$ and $\left(4,2\right)$ has same first element.

Here every ordered pair don’t have different input for every output.

So, the relation is not the function.