Q12. - Algebra 2

Question

Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function.

$y=2x+1$

Step-by-Step Solution

Answer

The graph of the relation is as shown:

The domain of the equation is $\left\{0,1,2\right\}$.

The range of the equation is $\left\{1,3,5\right\}$.

The relation or equation is a function.

Step 1 – Simplifying the following equation

$y=2x+1$

We will put different values of x to find the value of y

Put $x=0$:

$\begin{array}{l}y=2x+1\\ y=2\left(0\right)+1\\ y=1\end{array}$

Put $x=1$:

$\begin{array}{l}y=2x+1\\ y=2\left(1\right)+1\\ y=3\end{array}$

Put $x=2$:

$\begin{array}{l}y=2x+1\\ y=2\left(2\right)+1\\ y=5\end{array}$

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

Step 2– Determining the domain of the equation

The domain is the set of all first elements of the ordered pairs

Hence, the domain will be $\left\{0,1,2\right\}$.

Step 3 - Determining the range of the equation

The range of a relation is the set of the second coordinates from the ordered pairs.

Hence, the range will be $\left\{1,3,5\right\}$.

Step 4 - Determining whether the relation is a function

This relation is a function because each element in the domain $\left\{0,1,2\right\}$ is paired with exactly one element in the range $\left\{1,3,5\right\}$.

Graphical Interpretation

The graph of the following function is: