Chapter 1, Problem 1RE

In Problems 1 and 2, determine whether each relation represents a function. For each function, state the domain and range.

$\left\{\left(-1,\text{ 0}\right),\left(2,\text{ 3}\right),\left(4,\text{ 0}\right)\right\}$

To determine

Whether the provided relation is function or not and state the domain and range.

Answer to Problem 1RE

Solution:

The provided relation is a function. The domain of this relation is $\left\{-1,2,4\right\}$, and its range is $\left\{0,3\right\}$.

Explanation of Solution

Given:

It is provided in the problem that the relation of the sets is $\left\{\left(-1,0\right),\left(2,3\right),\left(4,0\right)\right\}$.

Formula used:

Definition: Let $X$ and $Y$ be two nonempty sets, A function from $X$ into $Y$ is a relation that associates with each elements of $X$ exactly one element of $Y$.

The set $X$ is called the domain of the function. For each element $x$ in $X$, the corresponding element $y$ in $Y$ is called the value of the function at $x$, or the image of $x$. The set of all images of the elements in the domain is called the range of the function.

The inputs of the provided sets are $-1,2$ and 4. The outputs are 0,3 and 0

This relation is a function because there are no ordered pairs with the same first element and different second elements.

The domain of this relation is $\left\{-1,2,4\right\}$, and its range is $\left\{0,3\right\}$.