Q27. - Algebra 2

Question

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

Then determine whether the relation or equation is a function.

 

$\left\{\left(0,-1.1\right),\left(2,-3\right),\left(1.4,2\right),\left(-3.6,8\right)\right\}$

Step-by-Step Solution

Answer

The graph of the given relation is:

The domain of the given relation is $\left\{-3.6,1.4,0,2\right\}$ and the range is $\left\{-3,-1.1,2,8\right\}$. 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 $\left\{\left(0,-1.1\right),\left(2,-3\right),\left(1.4,2\right),\left(-3.6,8\right)\right\}$.

Plot the ordered pairs $\left(0,-1.1\right),\left(2,-3\right),\left(1.4,2\right),\left(-3.6,8\right)$ on a coordinate plane as shown below:

Step 3 – Domain and range of the given relation.

Input values of the relation are $-3.6,1.4,0,2$ and the output values are $-3,-1.1,2,8$.

Domain $=\left\{-3.6,1.4,0,2\right\}$

Range $=\left\{-3,-1.1,2,8\right\}$

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 $\left\{-3.6,1.4,0,2\right\}$ and the range is $\left\{-3,-1.1,2,8\right\}$. The relation is a function.