Q25. - Algebra 2

Question

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

Then determine whether the relation or equation is a function.

 

$\left\{\left(-2,5\right),\left(3,7\right),\left(-2,8\right)\right\}$

Step-by-Step Solution

Answer

The graph of the given relation is:

The domain of the given relation is $\left\{-2,3\right\}$ and the range is $\left\{5,7,8\right\}$. The relation is not 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 $\left\{\left(-2,5\right)\text{,}\left(\text{3,7}\right)\text{,}\left(-2,8\right)\right\}$.

Plot the ordered pairs $\left(-2,5\right)\text{,}\left(\text{3,7}\right)\text{,}\left(-2,8\right)$ on a coordinate plane as shown below:

Step 3 – Domain and range of the given relation.

Input values of the relation are -2,3 and the output values are 5,7,8.

Domain $=\left\{-2,3\right\}$

Range $=\left\{5,7,8\right\}$

Step 4 – Check whether the relation is a function.

This relation is not a function because -2 in the domain is paired with both 5 and 8 in the range.

 

Thus, the domain of the given relation is $\left\{-2,3\right\}$ and the range is $\left\{5,7,8\right\}$. The relation is not a function.