Q7. - Algebra 2

Question

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

Then determine whether the relation or equation is a function.

 

$\{(7,8),(7,5),(7,2),(7,-1)\}$

Step-by-Step Solution

Answer

The graph of the given relation is:

The domain of the given relation is $\left\{7\right\}$ and the range is $\left\{-1,2,5,8\right\}$. 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 $\left\{\left(7,8\right),\left(7,5\right),\left(7,2\right),\left(7,-1\right)\right\}$.

Plot the ordered pairs $\left(7,8\right),\left(7,5\right),\left(7,2\right),\left(7,-1\right)$ on a coordinate plane as shown below:

Step 3 – Domain and range of the given relation.

Input value of the relation is 7 and the output values are $8, 5, 2, -1$.

Domain $=\left\{7\right\}$

Range $=\left\{-1,2,5,8\right\}$

Step 4 – Check whether the relation is a function.

This relation is not a function because 7 in the domain is paired with all $8, 5, 2, -1$ in the range.

                       

Thus, the domain of the given relation is $\left\{7\right\}$ and the range is $\left\{-1,2,5,8\right\}$. The relation is not a function.