Q26. - Algebra 2

Question

Graph each relation or equation and find the domain and range. 

Then determine whether the relation or equation is a function.

 

$\left\{\left(3,4\right),\left(4,3\right),\left(6,5\right),\left(5,6\right)\right\}$

Step-by-Step Solution

Answer

The graph of the given relation is:

The domain of the given relation is $\left\{3,4,5,6\right\}$ and the range is $\left\{3,4,5,6\right\}$. The relation is a function.

Step 1 – Definition of function, domain and range.

• A relation is a function if each element of the domain is paired with exactly one element of the range and a relation is not a function if there exist an element in the domain paired with more than one element of the range.
• The set of input values is known as domain.
• The set of output values is known as Range.

Step 2 – Draw the graph of the given relation.

The given relation is $\left\{\left(\text{3,4}\right)\text{,}\left(\text{4,3}\right)\text{,}\left(\text{6,5}\right),\left(5,6\right)\right\}$.

Plot the ordered pairs $\left(\text{3,4}\right)\text{,}\left(\text{4,3}\right)\text{,}\left(\text{6,5}\right),\left(5,6\right)$ on a coordinate plane as shown below:

Step 3 – Domain and range of the given relation.

Input values of the relation are 3,4,5,6 and the output values are 3,4,5,6.

Domain $=\left\{3,4,5,6\right\}$

Range $=\left\{3,4,5,6\right\}$

Step 4 – Check whether the relation is a function.

This relation is a function because each number of the domain is paired with exactly one member of the range.

 

Thus, the domain of the given relation is $\left\{3,4,5,6\right\}$ and the range is $\left\{3,4,5,6\right\}$. The relation is a function.