Question

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

52. $x=-5y+2$

Short answer

Graph of given equation is

Domain is $\mathrm{ℝ}$ and range is $\mathrm{ℝ}$

Given equation is a function.

Step-by-step solution

- Plot given equation

First find $x\text{-intercept}$ by substituting 0 for y

$\begin{array}{c}x=-5\left(0\right)+2\\ x=2\end{array}$

$x\text{-intercept}$is $\left(2,0\right)$

Now find $y\text{-intercept}$by substituting 0 for x

$\begin{array}{c}0=-5y+2\\ 5y=2\\ y=0.4\end{array}$

$y\text{-intercept}$is $\left(0,0.4\right)$

Using these two points plot the line of given equation as shown below

$y\text{-intercept}$

- Find the domain and range

Domain is the set of pre-images x and range is set of images y

As both x and y are defined for all real number so domain is $\mathrm{ℝ}$ and range is $\mathrm{ℝ}$

- To determine given equation is function or not

Since, for every x only one value exist, so given equation is a function.