Q11. - Algebra 2

Question

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

$y=0.5x$

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$\left\{0,0.5,1\right\}$.

The relation or equation is a function.

Step 1 – Simplifying the following equation

$y=0.5x$

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

Put$x=0$:

$\begin{array}{l}y=0.5x\\ y=0.5\left(0\right)\\ y=0\end{array}$

Put$x=1$:
$\begin{array}{l}y=0.5x\\ y=0.5\left(1\right)\\ y=0.5\end{array}$

Put$x=2$:

$\begin{array}{l}y=0.5x\\ y=0.5\left(2\right)\\ y=1\end{array}$
$\therefore \left\{\left(0,0\right),\left(1,0.5\right),\left(2,1\right)\right\}$

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 $\left\{0,0.5,1\right\}$.

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 $\left\{0,0.5,1\right\}$

Graphical Interpretation

The graph of the following function is: