Q28. - Algebra 2

Question

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

Then determine whether the relation or equation is a function.

 

$\left\{\left(-2.5,1\right),\left(-1,-1\right),\left(0,1\right),\left(-1,1\right)\right\}$

Step-by-Step Solution

Answer

The graph of the given relation is:

The domain of the given relation is $\left\{-2.5,-1,0\right\}$ and the range is $\left\{-1,1\right\}$. 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 $\left\{\left(-2.5,1\right)\text{,}\left(-1,-1\right)\text{,}\left(0,1\right),\left(-1,1\right)\right\}$.

Plot the ordered pairs $\left(-2.5,1\right)\text{,}\left(-1,-1\right)\text{,}\left(0,1\right),\left(-1,1\right)$ on a coordinate plane as shown below:

Step 3 – Domain and range of the given relation.

Input values of the relation are -2.5,-1,0 and the output values are -1,1.

Domain $=\left\{-2.5,-1,0\right\}$

Range $=\left\{-1,1\right\}$

Step 4 – Check whether the relation is a function.

This relation is not a function because -1 in the domain is paired with both -1 and 1 in the range.

 

Thus, the domain of the given relation is $\left\{-2.5,-1,0\right\}$ and the range is $\left\{-1,1\right\}$. The relation is not a function.