Q23. - Algebra 2

Question

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

Then determine whether the relation or equation is a function.

 

$\left\{\left(2,1\right),\left(-3,0\right),\left(1,5\right)\right\}$

Step-by-Step Solution

Answer

The graph of the given relation is:

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

Plot the ordered pairs $\left(\text{2,1}\right)\text{,}\left(-3,0\right)\text{,}\left(\text{1,5}\right)$ on a coordinate plane as shown below:

Step 3 – Domain and range of the given relation.

Input values of the relation are $-3,1,2$ and the output values are 0,1,5.

Domain $=\left\{-3,1,2\right\}$

Range $=\left\{0,1,5\right\}$

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 $\left\{-3,1,2\right\}$ and the range is $\left\{0,1,5\right\}$. The relation is a function.