Q1. - Algebra 2

Question

State the domain and range of the relation $\left\{\left(\mathbf{2},\mathbf{5}\right),\left(-\mathbf{3},\mathbf{2}\right),\left(\mathbf{2},\mathbf{1}\right),\left(-\mathbf{7},\mathbf{4}\right),\left(\mathbf{0},-\mathbf{2}\right)\right\}$

Step-by-Step Solution

Answer

The domain of the given relation is $\left\{-7,-3,0,2\right\}$ and the range of the given relation is $\left\{-2,1,2,4,5\right\}$.

Step 1 – State the concept

A relation is a set of ordered pairs, The domain is the set of all first coordinates from the ordered pairs and the range is the set of all second coordinates from the ordered pairs.

Step 2 – List the given data

The relation $\left\{\left(2,5\right),\left(-3,2\right),\left(2,1\right),\left(-7,4\right),\left(0,-2\right)\right\}$.

Step 3 – State the domain

The set of all first coordinates from the ordered pairs of the given relation is $\left\{2,-3,2,-7,0\right\}$.
Writing duplicate elements once and arranging in ascending order, the set is $\left\{-7,-3,0,2\right\}$.
This is the domain of the given relation.

Step 4 – State the range

The set of all second coordinates from the ordered pairs of the given relation is $\left\{5,2,1,4,-2\right\}$.
Arranging the elements in ascending order, the set is $\left\{-2,1,2,4,5\right\}$.
This is the range of the given relation.